  We present observations of the HD 15115 debris disk from ALMA at 1.3 mm that
capture this intriguing system with the highest resolution
($0.\!\!^{\prime\prime}6$ or $29$ AU) at millimeter wavelengths to date. This
new ALMA image shows evidence for two rings in the disk separated by a cleared
gap. By fitting models directly to the observed visibilities within a MCMC
framework, we are able to characterize the millimeter continuum emission and
place robust constraints on the disk structure and geometry. In the best-fit
model of a power law disk with a Gaussian gap, the disk inner and outer edges
are at $43.9\pm5.8$ AU ($0.\!\!^{\prime\prime}89\pm0.\!\!^{\prime\prime}12$)
and $92.2\pm2.4$ AU ($1.\!\!^{\prime\prime}88\pm0.\!\!^{\prime\prime}49$),
respectively, with a gap located at $58.9\pm4.5$~AU
($1.\!\!^{\prime\prime}2\pm0.\!\!^{\prime\prime}10$) with a fractional depth of
$0.88\pm0.10$ and a width of $13.8\pm5.6$ AU
($0.\!\!^{\prime\prime}28\pm0.\!\!^{\prime\prime}11$). Since we do not see any
evidence at millimeter wavelengths for the dramatic east-west asymmetry seen in
scattered light, we conclude that this feature most likely results from a
mechanism that only affects small grains. Using dynamical modeling and our
constraints on the gap properties, we are able to estimate a mass for the
possible planet sculpting the gap to be $0.16\pm0.06$ $M_\text{Jup}$.
