We present a measurement of the lifetime of ground state atomic carbon, C(3P), against ionization processes in interplanetary space and compare it to the lifetime expected from the dominant physical processes likely to occur in this medium. Our measurement is based on analysis of a far ultraviolet (FUV) image of comet C/2004 Q2 (Machholz) recorded by the Galaxy Evolution Explorer (GALEX) on 2005 March 1. The bright C i 1561 Å and 1657 Å multiplets dominate the GALEX FUV band. We used the image to create high signal-to-noise ratio radial profiles that extended beyond 1 × 106 km from the comet nucleus. Our measurements yielded a total carbon lifetime of (7.1–9.6) × 105 s (ionization rate of (1.0–1.4) × 10−6 s−1) when scaled to 1 AU. This compares favorably to calculations assuming solar photoionization, solar wind proton change exchange, and solar wind electron impact ionization are the dominant processes occurring in this medium and that comet Machholz was embedded in the slow solar wind. The shape of the C i profiles inside 3 × 105 km suggests that either the CO lifetime is shorter than previously thought and/or a shorter-lived carbon-bearing parent molecule, such as CH4, is providing the majority of the carbon in this region of the coma of comet Machholz.