The first line of Hurston's essay reads:

I am colored but I offer nothing in the way of extenuating circumstances except the fact that I am the only Negro in the United States whose grandfather on the mother's side was not an Indian chief.

Hurston says this to set a humorous tone for this essay. Her writing celebrates blackness as part of the brilliant variety of American life. The humor in the first line works on several levels. To begin with, it has a biting edge: it is significant that Hurston states that everyone's grandfather on the mother's side was an Indian Chief. "Indian Chief" is a euphemism for "white master:" this is an allusion to the commonly understood idea that white owners raped their black female slaves to create more slaves, especially after the import of slaves from Africa was banned in the US. Hurston makes this comment to establish from the start that the races are more mixed than people like to acknowledge—and that racial categories should therefore hold less weight.

Second, black people in her era used non-black ancestry to try to bolster their status. Hurston was quite aware that light-skinned black people were more desirable marriage partners than those with darker skin in the period when she wrote. Hurston, however, is rejecting any idea that she should try to enhance her status by alluding to white or Native ancestry. She is who she is and proud of it.

Hurston emphasizes the point about racial mixing in a different way at the end of the essay, when she talks about feeling like a brown bag jumbled with objects inside sitting next to yellow, white, and red bags with similar mixes of goods within. Hurston says that if the bags were emptied into one big pile and redistributed into each bag again, it would not make much difference what items went into which bag:

A bit of colored glass more or less would not matter.

Hurston is asserting, years before it became common to think so, that race is a social construct that shouldn't make much of a difference in how people are treated. She believes that we are all a mix.

There has been a tradition in both black and white cultures in America to claim a significant ancestor of Native American ancestry. Reasons for these claims vary from family to family, but even when no clear or identifiable ancestor presents as evidence, many families cling to this belief. See the link below from another writer who reflects on Zora Neale Hurston's words and then examines his own family's claims compared to DNA testing.

In this opening line, Hurston claims the strength in being "just" colored (the term she uses to describe herself in the introduction). She does not lean into claims of other ancestry and notes with humor that this separates her from others who are racially similar to her. To be African American is enough, and she feels no need to minimize her racial ancestry in an effort to claim to be anything else.

Hurston elaborates further on these feelings a bit later in the piece:

I do not always feel colored. Even now I often achieve the unconscious Zora of Eatonville before the Hegira. I feel most colored when I am thrown against a sharp white background.

For instance at Barnard. “Beside the waters of the Hudson” I feel my race. Among the thousand white persons, I am a dark rock surged upon, and overswept, but through it all, I remain myself.

Hurston is a confident woman, proud of her race and its unique history—and that is the ultimate connotation of her opening line.

As the previous educators mentioned, Hurston is poking fun at the common belief among many black Americans, which existed both in 1928 when she published the essay and which persists to date, that they have indigenous ancestry. It is, of course, true that some African Americans have Native American ancestry, though recent research by the historian Henry Louis Gates Jr. has shown that most who have such ancestry only have 1-2%, indicating that the ancestor showed up in their family tree sometime in the eighteenth century. African Americans from Oklahoma with indigenous ancestry, Gates discovered, tended to have closer to five percent. It is important to note that the eastern indigenous tribes who made up what was named the Five Civilized Tribes, including the Cherokee, Creek, Choctaw, Chickasaw, and the Seminole, were forced by Andrew Jackson's administration to move to Oklahoma on the Trail of Tears in the 1830s and 1840s. This provides the historical context of Hurston's comment, but the reason for her comment is more complex and less certifiable.

It is possible that some black people identified as "part Indian" or claimed to have "Indian in the family" as a way to distance themselves from blackness. Historically, indigenous people were regarded as "savages" but were also deemed more assimilable than black people. Thomas Jefferson expressed such a view in Notes on the State of Virginia. However, it is likely that the claim of indigenous ancestry was also an attempt to explain the bestowal of European features as not the result of a slave master's rape of a slave woman, but as the result of a consensual coupling between two people from two oppressed cultures. Sometimes, storytelling is a way to cope with pain.

Hurston, being an astute cultural critic and a trained anthropologist, was probably aware of all of the reasons why many black people claimed Native American ancestry. She was probably also aware that such claims are equally common among white people as an attempt to distance themselves from a racist legacy. Hurston's comment was certainly not malicious; it merely found the humor in apocryphal family legends.