We report precision measurements of the excited state lifetime of the $5p$ $^2P_{1/2}$ and $5p$ $^2P_{3/2}$ levels of a single trapped Cd$^+$ ion. The ion is excited with picosecond laser pulses from a mode-locked laser and the distribution of arrival times of spontaneously emitted photons is recorded. The resulting lifetimes are 3.148 $pm$ 0.011 ns and 2.647 $pm$ 0.010 ns for $^2P_{1/2}$ and $^2P_{3/2}$ respectively. With a total uncertainty of under 0.4%, these are among the most precise measurements of any atomic state lifetimes to date.
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