  We show that the $P\sim8\,{\rm h}$ photometric period and the astrometrically
measured $A_{\rm ng}\sim2.5\times10^{-4}\,{\rm cm\,s^{-2}}$ non-gravitational
acceleration (at $r\sim1.4\,{\rm AU}$) of the interstellar object 1I/2017
(`Oumuamua) can be explained by a nozzle-like venting of volatiles whose
activity migrated to track the sub-solar location on the object's surface.
Adopting the assumption that `Oumuamua was an elongated $a\times b \times c$
ellipsoid, this model produces a pendulum-like rotation of the body and implies
a long semi-axis $a\sim 5A_{\rm ng}P^2/4\pi^2 \sim 260\,{\rm m}$. This scale
agrees with the independent estimates of `Oumuamua's size that stem from its
measured brightness, assuming an albedo of $p\sim0.1$, appropriate to ices that
have undergone long-duration exposure to the interstellar cosmic ray flux.
Using ray-tracing, we generate light curves for ellipsoidal bodies that are
subject to both physically consistent sub-solar torques and to the time-varying
geometry of the Sun-Earth-`Oumuamua configuration. Our synthetic light curves
display variations from chaotic tumbling and changing cross-sectional
illumination that are consistent with the observations, while avoiding
significant secular changes in the photometric periodicity. If our model is
correct, `Oumuamua experienced mass loss that wasted $\sim 10\%$ of its total
mass during the $\sim 100\,{\rm d}$ span of its encounter with the inner Solar
System and had an icy composition with a very low $[{\rm C}/{\rm O}]\lesssim
0.003$. Our interpretation of `Oumuamua's behavior is consistent with the
hypothesis that it was ejected from either the outer regions of a planetesimal
disk after an encounter with an embedded $M_{\rm p} \sim M_{\rm Nep}$ planet or
from an exo-Oort cloud.
