We study genome-wide nucleotide diversity in three subspecies of extant chimpanzees using exome capture. After strict filtering, SNVs and indels were called and genotyped for >50% of exons at a mean coverage of 35x per individual. Central chimpanzees (P. t. troglodytes) are the most polymorphic (nucleotide diversity, θw= 0.0023 per site) followed by Eastern (P. t. schweinfurthii) chimpanzees (θw = 0.0016) and Western (P. t. verus) chimpanzees (θw = 0.0008). A demographic scenario of divergence without gene flow fits the patterns of autosomal synonymous nucleotide diversity well except for a signal of recent gene flow from Western into Eastern chimpanzees. The striking contrast in X-linked vs. autosomal polymorphism and divergence previously reported in Central chimpanzees is also found in Eastern and Western chimpanzees. We show that the direction of selection (DoS) statistic exhibits a strong non-monotonic relationship with the strength of purifying selection S, making it inappropriate for estimating S. We instead use counts in synonymous vs. non-synonymous frequency classes to infer the distribution of S coefficients acting on non-synonymous mutations in each subspecies. The strength of purifying selection we infer is congruent with the differences in effective sizes of each subspecies: Central chimpanzees are undergoing the strongest purifying selection followed by Eastern and Western chimpanzees. Coding indels show stronger selection against indels changing the reading frame than observed in human populations.