The story opens by describing a neighborhood in Brooklyn, New York, called Williamsburg. There is a certain kind of tree that grows throughout the neighborhood, called the Tree of Heaven by some, since it grows wherever its seeds land—in old lots, trash heaps, and even cement. It grows only in the tenement districts, where the poor people live.
Francie Nolan has such trees in her yard in Williamsburg. The story opens on a Saturday, which always means a trip to the junkie for eleven-year-old Francie and her brother, Neeley. Carney the junkie pays the neighborhood kids pennies for the bits of tin foil and other metals that come from such junk as cigarette packs and jar lids. He likes girls better than boys, and so Francie delivers the junk for herself and her brother. She earns sixteen cents and a "pinching penny"—the extra penny Carney gives if a girl doesn't shrink when he pinches her cheek. Neeley handles the money, taking out half for the tin-can bank; the rest they divide evenly, except that Francie always keeps the pinching penny.
The two children then make their way to Cheap Charlie's, the penny candy store. Francie doesn't go inside, adhering to the unwritten rule that it is a boys' store. Here the children pay a penny to draw a number for a prize. Francie has never heard of anyone getting the good prizes-roller skates or baseball mitts or dolls. After accompanying her friend Maudie Donavan to Gimpy's candy store, she goes on to the five and dime, where she is privileged to touch the merchandise because she is buying, and decides on five cents worth of pink and white peppermints. Francie walks back home, noticing the pushcarts and smells of her neighborhood. She muses that Jewish women must have so many babies because they are hopeful that one will be the messiah, and that Irish women just looked ashamed at being pregnant.
Katie Nolan, Francie's mom, arrives home soon after her daughter, having finished her week's work scrubbing floors. She is slight and pretty and fun. The narrator also mentions that Francie's father has a drinking problem. Francie's mother sends her out to buy bread and tongue, and at Francie's pleading, sweet buns for dessert, since it is Saturday.
Francie meets up with Neeley and they return home to have lunch with Mama. Coffee is a luxury in the Nolan household, and each member of the family is allowed three cups per day, with milk. Katie Nolan believes that Francie is entitled to throw her cups down the drain, if she wishes, saying that it's good for poor people like them to be able to waste something.
After dinner, Mama sends Francie back for bread from Losher's, where the stale loaves are sold to the poor. While Francie is waiting, she stares at an old man and is suddenly frightened by his disfigurement, especially his feet. Francie then fights the crowd, and buys her bread. Once outside, she sees a baby and imagines its foot as an old person's foot, and panics again.