ZooKeeper is a high-performance coordination service for distributed applications. The official Python client is a C extension which does not play well with asynchronous frameworks such as gevent due to its use of real threads. kazoo is a wrapper client which uses IO tricks to be async compatible. It also attempts to present a more pythonic interface than zkpython.
Initially kazoo only supports gevent as well as non-async environments.
Kazoo depends on the ZooKeeper python binding. Because this can be installed in various ways, it is not a listed Python dependency of kazoo. The ZK bindings should be installed from your distribution if possible. Otherwise the unofficial zc-zookeeper-static package is easy to install via PyPi.