Chapter 4 ends with Scout revealing that she heard laughter coming from Boo Radley's house on the day she rolled into the yard. Why might Harper Lee have chosen to save this detail for the end of the chapter, instead of sharing it right after the incident occurs in the book?

There are several reasons for why Harper Lee may have chosen to save this detail for the end of the chapter, instead of sharing it right after the incident occurs.
First, it makes for a dramatic ending to Chapter 4. This dramatic ending is also Lee's very creative way of telling us that Boo Radley really does exist. From the text in chapters 1, 2, and 3, we may be led to conclude that Boo Radley only exists in Scout, Jem, and Dill's imaginations. These early chapters seem to portray Boo as a fantasy figure.

The Radley Place was inhabited by an unknown entity the mere description of whom was enough to make us behave for days on end . . .
Inside the house lived a malevolent phantom. People said he existed, but Jem and I had never seen him. People said he went out at night when the moon was down, and peeped in windows. When people’s azaleas froze in a cold snap, it was because he had breathed on them. Any stealthy small crimes committed in Maycomb were his work.

We are told that the entire Radley clan keeps to itself and in fact, none of the family members attend church, "a predilection unforgivable in Maycomb." In other words, the Radley family is quite happy to disregard the conventions of polite Southern society. Out of this eccentricity is born the legendary Radley narrative, with all the elements inherent in a typical Southern folktale.
Scout (narrating as her mature self) tells us about the Radley legend. Accordingly, the youngest Radley son fell in with the wrong crowd (the Cunninghams from Old Sarum). The boys supposedly locked the town beadle, Mr. Conner, in the courthouse outhouse. The judge then sentenced the boys to attend the state industrial school. However, Mr. Radley asked for his son to be released into his custody. We are then told the hair-raising tale of how Boo supposedly thrust a pair of scissors into Mr. Radley's leg. After this unsavory event, there is talk about an asylum and of Boo being locked up, and according to Jem, tied to the bed against his will.
By framing the Radley legend as an intrinsic part of the story, Lee allows us to see how the oral tradition shapes Scout and Jem's childhoods. Through the prism of the Southern oral tradition and a larger-than-life character (Boo Radley), we are taken back in time to Lee's South, a land of entrenched social hierarchies and traditions. In that South, both black and white knew each other's duties and obligations; those who did not or who chose not to accept the status quo were usually marginalized, vilified, and rejected. Yet, Southern tradition has always revered the mythical figure who transcends social strictures to effect societal change. Boo represents this figure, a man who makes an indelible mark on Scout and Jem's lives.
At the end of chapter 4, Scout reveals why she wants to stop playing the Radley game: she had heard Boo Radley laugh, and she now knows that he most assuredly does exist. This revelation is an important one, for it foreshadows Boo's later (and very unconventional) actions on Scout and Jem's behalf. Despite being one of Maycomb's outcasts, Boo saves Scout and Jem from the diabolical Bob Ewell.
So, it can be argued that Lee chose to reveal Boo's laughter at the end of chapter 4 for these reasons:
1) To make a dramatic revelation: Boo Radley is not just a figment of Scout and Jem's imaginations. He's an actual, though uncomfortable, part of Maycomb's reality.
2) To highlight the Southern reverence for the oral tradition, as encompassed in tall tales about larger-than-life characters, and how the actions of these characters affect society.
3) To emphasize the importance of Boo's laughter to the story. Lee chose to save this detail for the end of the chapter so that the point would not be lost: Boo's humanity is Maycomb's saving grace. He is one of the mockingbirds of the story, destined to bring good to others. It is Boo's humanity that saves Scout and Jem, and in the end, it is the only thing that stands between them and the destructive racism that threatens to engulf them in its fiery flames.