Superconductivity was discovered in the narrow-gap semiconductor CsBi4Te6. A superconducting transition around 4.4 K was observed for p-type samples in temperature-dependent resistivity and magnetic susceptibility data Stoichiometric CsBi4Te6 is not a superconductor. A remarkably high critical field of similar to 10 T was estimated from the field dependent resistivity data The strongly anisotropic CsBi4Te6 system is monoclinic and the first member of a larger homologous series Cs-4[Bi2n+4Te3n+6] that exhibits unconventional superconductivity, suggesting that proper doping of the homologous series may create a novel class of superconductors from semiconductors.