  We present the highest resolution (1") $^{12}$CO(1-0) observations of
molecular gas in the dwarf starburst galaxy NGC 625, to date, obtained with
ALMA. Molecular gas is distributed in discrete clouds within an area of $0.4$
kpc$^2$ and does not have well-ordered large-scale motions. We measure a total
molecular mass in NGC 625 of $5.3\times 10^6 M_\odot$, assuming a Milky Way
CO-to-H$_2$ conversion factor. We use the CPROPS package to identify molecular
clouds and measure their properties. The 19 resolved CO clouds have a median
radius of 20 pc, a median line width 2.5 km s$^{-1}$, and a median surface
density of 169 $M_\odot$pc$^{-2}$. Larson scaling relations suggest that
molecular clouds in NGC 625 are mostly in virial equilibrium. Comparison of our
high-resolution CO observations with a star formation rate map, inferred from
ancillary optical observations observations, suggests that about 40% of the
molecular clouds coincide with the brightest HII regions. These bright HII
regions have a range of molecular gas depletion timescales, all within a factor
of $\sim 3$ of the global depletion time in NGC 625 of 106-134 Myr. The highest
surface density molecular clouds towards the southwest of the galaxy, in a
region we call the Butterfly, do not show strong star formation activity and
suggest a depletion time scale longer than 5 Gyr.
