How does the World State's motto fit the society described in chapter 1 of Brave New World?
The motto of the World State is "Community, Identity, Stability."
The society described in Chapter One is a very carefully engineered and planned one. In this way, a community has been developed to be both stable and to reinforce group identity. The five main groups of people, Alphas, Betas, Gammas, Deltas and Epsilons are carefully socialized to identify with each other and to not want to belong to another group. They are trained from early childhood to reject the other groups and to find good only in things which are available to them. This leads inevitably to stability.
Every group has its own set of jobs and rules, and all members learn to find happiness within the group they have been born to. The idea of keeping people happy to keep them controlled leads also to stability. Later in the book, this idea of absence of pain and sorrow is questioned by the outsider John. But everything in Chapter One is set up to adhere to the motto.