church-oriented, mostly low-quality literature into brilliant irony. 

That's Chaucer.  That's why he's still in the text books.  That's why his works are a big step toward modern literature.

Well, for starters, Chaucer is not a Modern Poet. Modernism began in the late 19th century and lasted up until about World War I, but those dates vary. However, I’m always one for using techniques, theories and criticism of one period to analyze texts of another. In fact, it would be in the spirit of Modernism, and even more in Postmodernism, to revisit older texts with these newer historical perspectives.

So, we are either looking at Chaucer’s work through Modernist lenses (as pretentious as that sounds) or we could just pretend that Chaucer is alive and writing today or during the Modernism period, so let’s just do that. What does he do that is characteristically Modern or ‘modern’ in the more general sense of our present time, 2011?

First thing he does that is characteristically modern is having multiple narrators. His work would probably be created to someone like William Faulkner who redefined narrative with his use of multiple narrators. You could also note his cultural diversity in presenting different speech patterns according to different social classes (the Knight is more eloquent than the Pardoner). Maybe you could go so far to say that Chaucer was making an allegorical comment on social classes and come to the conclusion that Chaucer employing a Marxist analysis of a Feudal system in 14th century England; and this wandering and storytelling was an alternative to facing the lack of possible upward mobility. Ok, so this may be a stretch, but that’s the point.

The theme of Christianity is prevalent and you could compare that to a resurgence of fundamental Christians in the political right in America and the emergence of religious fundamentalism in other parts and other religions of the world. If you go this route, (still pretending that Chaucer is writing today), maybe Chaucer is mocking them in a satire; or maybe he’s promoting them. But satire is more fun.

In the Nun’s Priest’s Tale, he uses animals to tell the story. There is nothing essentially Modern or Ancient about this. So, what Modern works do this? Disney movies? Cartoons? Adult Swim?

Pretending aside, Chaucer is still being read and discussed. This makes him, by definition, a Modern poet because he is still relevant. If he wasn’t relevant he wouldn’t be read or discussed. Living in the modern world, today’s readers can’t help but read him with a Modernist bias. In other words, it is difficult (maybe impossible) to read Chaucer as a 14th century Englander. You can’t help but put your own spin on any historical text you read. This is the premise of New Historicism. The goal is to separate the Modern conceptions of Chaucer’s work and what his work meant in its own context, in its own time.

Geoffrey Chaucer is known primarily not only as a poet, but also as a man with an extraordinary gift of looking at his subjects and the context of the time in which they live to provide an unparalleled vision into the daily existence of medieval persons from all walks of life and social strata. His "shrewd observations" brought alive some of literature's most memorable characters.

Though Chaucer came from humble beginnings himself, the variety of professions in which he was employed exposed him to all kinds of people. It was, however, his keen sense of observation through which he was able to make the best use of his myriad of experiences.

Another compelling aspect of Chaucer's work is that rather than writing in the language popular to the time (Latin—the Roman Church's language) or French (the language of royalty and nobility—after the conclusion of Norman invasion of England by William the Conqueror around 1066), Chaucer wrote in the language of Middle English allowing that the common people (the emerging middle class) would have access to his work. 

And if that is not enough, Chaucer was completely honest about what he witnessed in the behaviors of a wide variety of people from many classes.

For instance, in The General Prologue to the Canterbury Tales, the Knight is held up as a man of humility and nobility of character. He fought for what he believed in as if it were his life's breath, but rather than receiving accolades for his work, he returned home to immediately take a pilgrimage in order to give thanks to God. Chaucer greatly admires the Knight:

There with us was a KNIGHT, a worthy man

Who, from the very first time he began  

To ride about, loved honor, chivalry,

The spirit of giving, truth and courtesy.

On the other hand, Chaucer was also brutally honest about the servants of the Church. All but one of his characters that serve the Church demonstrates the worst possible behavior. The Pardoner, for example, sells "hot" (stolen) pardons, to the poorest of people—most living in poverty—which believe their sins will be forgiven for purchasing the pardons. Also:

...in his bag he had a pillowcase

That used to be, he said, Our Lady's veil;

He claimed he had a fragment of the sail

That took Saint Peter out upon the sea

Before Christ called him to his ministry…

The Friar is more interested in the ladies, and in hunting and singing. As servants of the Church were expected to put away worldly goods and practices and serve as shepherds to God's flock, neither the Friar, the Pardoner nor the Nun (the Prioress) does so. Only the Parson was a worthy man of the Church. Chaucer allows the reader to see that though he has little, he gives what he has to the poor, following the true meaning of the "servant" to his flock.

However, in the manner of a true and gifted poet, Chaucer never tells the members of his audience what they should think. He presents the facts and allows the reader to draw his/her own conclusions regarding the characters he presents.

In terms of Chaucer's work from a structural standpoint, Chaucer specifically uses the pilgrimage as a framework: for this was perhaps the only event of that era when people of all backgrounds and classes would come together, enabling the author to present to the reader with a brilliant cross-section of society at that time.

Chaucer also changed the structure of the poem, something that would impact writers for generations to come:

Chaucer’s [poetic] practice established accentual syllabic meter as the norm of English verse for five centuries thereafter. Beginning with the four-stress lines of The Book of the Duchess and The House of Fame...Chaucer developed the five-stress line which became the backbone of the major poetry of William Shakespeare, John Milton, Alexander Pope, William Wordsworth, and many others.

Chaucer changed the face of literature, impacting what it has become for the modern-day poet. He was not afraid to be honest to his craft. He did not follow the prescribed methods of the day: he wrote in a language accessible to the masses. He inferred; he did not tell his reader what to think. (Chaucer pretends to be one of the members of the pilgrimage, thereby making himself a more credible source for his readers to offer his observations—another way in which he shows that he is a maverick of his day.) Additionally, Chaucer's diction (word choice) more easily allows the reader to weigh the character of each member of the pilgrimage. In this way, there was room for discussion and interpretation. He also introduces the use of a meter (rhythmic pattern) unfamiliar to audiences up to that point.

Chaucer is a modern poet in that he is not afraid to try something different. Also he is able to provide barely perceptible nuances that delve into the deepest and truest dispositions of his subjects. He uses excellent sensory details to create a world for the reader that is unfamiliar—moreover, he is able to bring to life (without personal judgment) characters that fairly fly off of the page.

In defining modern poetry, Kenneth Goldsmith, in his article entitled, "The Challenges of Twenty-first Century Writing," he notes:

Success lies in knowing what to include and — more important — what to leave out […] While all words may be created equal — and treated thusly — the way in which they’re assembled isn’t; it’s impossible to suspend judgment and folly to dismiss quality.

By referring to these more modern perceptions—even expectations—of a poet's responsibilities to his/her art, Chaucer (who started a new movement in poetry that influenced so many great authors that would follow him) seems to live up to these expectations. Perhaps it is because of the example that he set, that modern poets have such high expectancies. I believe that Chaucer would commend them for their efforts.

Additional source:

http://www.poetryfoundation.org/harriet/2010/04/the-challenges-of-twenty-first-century-writing/