One of the promises that George has fulfilled in chapter 3 is getting Lennie a small animal as his companion. Throughout their travels, Lennie has been asking for a small pet that can be with him and towards which he can provide love. In the first chapter, this is seen with the dead mouse he carries. Additionally, the entire dream that both men share only has relevance to Lennie because of the rabbits he wishes to own. In chapter 3, a small down payment on this promise has been given by George to Lennie via Slim. When Slim's dog ends up giving birth to puppies, Slim gives one to Lennie. This is something that George facilitated through Slim. This is one promise that George has maintained to Lennie, a small start of a larger dream both men share.
Another promise that George fulfills in chapter 3 is detailed in his discussions with Slim. The promise that George made to Lennie's Aunt Clara to look out for him and take care of him is what we understand as the tie that binds both men. George tells Slim about this promise to help explain why the two men are always together. George demonstrates himself as a man of his word and honoring this promise is revealed in his discussions with Slim in chapter 3. Coupled with George's promise to Lennie in getting him a small pet is reflective of how George honors his promises in chapter 3.