  We report a measurement of the lifetime of the 3d 2D_{5/2} metastable level
in 40Ca+, using quantum jumps of a single cold calcium ion in a linear Paul
trap. The 4s S_{1/2} - 3d D_{5/2} transition is significant for single-ion
optical frequency standards, astrophysical references, and tests of atomic
structure calculations. We obtain tau = 1.168 +- 0.007 s from observation of
nearly 64,000 quantum jumps during approximately 32 hours. Our result is more
precise and significantly larger than previous measurements. Experiments
carried out to quantity systematic effects included a study of a previously
unremarked source of systematic error, namely excitation by the broad
background of radiation emitted by a semiconductor diode laser. Combining our
result with atomic structure calculations yields 1.20 +- 0.01 s for the
lifetime of 3d D_{3/2}. We also use quantum jump observations to demonstrate
photon anti-bunching, and to estimate background pressure and heating rates in
the ion trap.
