Sleeping sickness, or Human African Trypanosomiasis, is a disease affecting the health and productivity of poor people in many rural areas of sub-Saharan Africa. The disease is caused by a single-celled flagellate, Trypanosoma brucei, which evades the immune system by periodically switching the proteins on its surface. We have produced a genome sequence for T. brucei gambiense, which is the particular subspecies causing most disease in humans. We compared this with an existing reference genome for a non-human infecting strain (T. b. brucei 927) to identify genes in T. b. gambiense that might explain its ability to infect humans and to assess how well the reference performs as a universal plan for all T. brucei. The genome sequences differ only due to rare insertions and duplications and homologous genes are over 95% identical on average. The archive of surface antigens that enable the parasite to switch its protein coat is remarkably consistent, even though it evolves very quickly. We identified genes with predicted cell surface functions that are only present in T. b. brucei and have evolved rapidly in recent time. These genes might help to explain variation in disease pathology between different T. brucei strains in different hosts.