Bi2Se3 is one of a handful of known topological insulators. Here we show that copper intercalation in the van der Waals gaps between the Bi2Se3 layers, yielding an electron concentration of approximately 2x10{20} cm{-3}, results in superconductivity at 3.8 K in CuxBi2Se3 for 0.12<or=x<or=0.15. This demonstrates that Cooper pairing is possible in Bi2Se3 at accessible temperatures, with implications for studying the physics of topological insulators and potential devices.