What happens in chapters 1–3 of Uncle Tom's Cabin?
Chapter 1 introduces the reader to the plot details that propel the story forward. That is a bit rare, since many novels usually only introduce the characters in the first few chapters, and then hit the reader with the story's central plot in chapter 3 or 4.
Chapter 1 introduces you to Arthur Shelby. He is a gentleman slave owner from Kentucky. He is negotiating a slave sale to Mr. Haley. Shelby wants to sell his slave Uncle Tom in order to get out of financial trouble. Mr. Haley wants a young slave boy too, so Mr. Shelby decides to sell a young slave boy named Harry. He is the son of Eliza, another slave on the property. Eliza witnesses the two men speaking with each other and begins to worry that her son will be sold.
Chapter 2 tells the reader that Eliza is married to an intelligent slave named George. We learn that George has invented a machine to help speed up factory work. Instead of being rewarded for his ingenuity, he was punished and given terrible work. A result of that was George couldn't see Eliza and Harry very much anymore.
In chapter 3 George is able to come to visit Eliza and Harry. He tells her of his plan to escape into Canada. From there he will earn enough money to buy Eliza's and Harry's freedom. Eliza doesn't want George to do it, but he won't be convinced.