We present a precise measurement of the lifetime of the 6(p) P-2(1/2)0 excited state of a single trapped ytterbium ion (Yb+). A time-correlated single-photon counting technique is used, where ultrafast pulses excite the ion and the emitted photons are coupled into a single-mode optical fiber. By performing the measurement on a single atom with fast excitation and excellent spatial filtering, we are able to eliminate common systematics. The lifetime of the 6p P-2(1/2)0 state is measured to be 8.12 +/- 0.02 ns, in good agreement with previous experimental measurements and some theoretical values.