We report the first operation of a Ra+ optical clock, a promising high-performance clock candidate. The clock uses a single trapped 226Ra+ ion and operates on the 7s 2S1/2 → 6d 2D5/2 electric quadrupole transition. By self-referencing three pairs of symmetric Zeeman transitions, we demonstrate a frequency instability of 1.1 x 10-13/√τ, where τ is the averaging time in seconds. The total systematic uncertainty is evaluated to be Δν/ν = 9 x 10-16. Using the clock, we realize the first measurement of the ratio of the D5/2 state to the S1/2 state Landé g-factors: gD/gS = 0.5988053(11). A Ra+ optical clock could improve limits on the time variation of the fine structure constant in an optical frequency comparison. The ion also has several features that make it a suitable system for a transportable optical clock.