Don Abbondio, parish priest at Lecco, has agreed to perform the marriage ceremony of Lorenzo and Lucia, two young peasants. The day before, as he is walking home, Abbondio is stopped by two “bravoes,” or elaborately dressed, armed men. The narrator includes a lengthy discourse on the history of this type of servant, including a royal prohibition on employing them. These two, who work for a local nobleman, Don Rodrigo, warn Abbondio not to marry the couple and not to reveal that the order came from Rodrigo; then they leave him. The narrator offers a large number of reasons that the less-than-courageous Abbondio could not expect help from the law.

He walks the rest of the way home, pondering how he might convince either one of the couple not to get married, but he cannot think of anything valid. At home, when his housekeeper, Perpetua, greets him, she recognizes how distressed he is. At first he refuses to say, telling her only that he has been sworn to silence, but she gives him a glass of wine and finally gets him to tell her. After revealing Rodrigo’s hand in the matter, Abbondio laments with Perpetua the improbability that anyone will believe him. They ponder their best course of action, then he leaves for his bedroom and exhorts her to keep silent.

Being Italy's most famous work of historical fiction, The Betrothed gives a good opportunity for a teacher to explain plot to students.  Chapter 1, that you ask about, is no exception in that it contains the exposition and the inciting incident (that some people call the conflict).  Please allow me to explain further.

In the first part of The Betrothed, we learn about Lucia and Renzo who live in a village near Lake Como, Italy.  We learn immediately why the novel is called The Betrothed because the two (Lucia and REnzo) are engaged to be married.  They want to be married in November of 1628.  Being Roman Catholic, the two lovers have contracted Father Don Abbondio to perform the ceremony. 

Unfortunately, the inciting incident happens when Father Don Abbondio is mugged by two men who give a stern warning for the priest not to perform the marriage of these two Italian lovers.  The reason is because Don Rodrigo (a prominent man in the community) forbids the union.  An important quotation that can relate to this very part is as follows:

Bullies, oppressors and all men who do violence to the rights of others are guilty not only of their own crimes, but also of the corruption they bring into the hearts of their victims.

Because the priest is afraid, he simply postpones the wedding and doesn't give a reason.  This upsets Renzo (of course), and Renzo convinces the priest to reveal the name of Don Rodrigo.  Of course, the real reason is that Don Rodrigo is also interested in Lucia and didn't want her to be married.

After chapter 1, the story continues and more interesting incidents about Lucia and Renzo and Don Rodrigo are revealed.