  We report the first operation of a Ra$^{+}$ optical clock, a promising
high-performance clock candidate. The clock uses a single trapped
$^{226}$Ra$^{+}$ ion and operates on the $7s\ ^2S_{1/2}\rightarrow$ $6d\
^2D_{5/2}$ electric quadrupole transition. By self-referencing three pairs of
symmetric Zeeman transitions, we demonstrate a frequency instability of
1.1$\times10^{-13}$/$\sqrt{\tau}$, where $\tau$ is the averaging time in
seconds. The total systematic uncertainty is evaluated to be ${\Delta \nu / \nu
= 9 \times 10^{-16}}$. Using the clock, we realize the first measurement of the
ratio of the $D_{5/2}$ state to the $S_{1/2}$ state Land\'{e} $g$-factors:
$g_{D}/g_{S}$ = 0.5988053(11). A Ra$^{+}$ optical clock could improve limits on
the time variation of the fine structure constant, $\dot \alpha / \alpha$, in
an optical frequency comparison. The ion also has several features that make it
a suitable system for a transportable optical clock.
