  The non-detection of a coma surrounding 1I/`Oumuamua, the first discovered
interstellar object (ISO), has prompted a variety of hypotheses to explain its
nongravitational acceleration. Given that forthcoming surveys are poised to
identify analogues of this enigmatic object, it is prudent to devise
alternative approaches to characterization. In this study, we posit X-ray
spectroscopy as a surprisingly effective probe of volatile ISO compositions.
Heavily ionized metals in the solar wind interact with outgassed neutrals and
emit high-energy photons in a process known as charge exchange, and charge
exchange induced X-rays from comets and planetary bodies have been observed
extensively in our Solar System. We develop a model to predict the X-ray flux
of an ISO based on its chemical inventory and ephemeris. We find that while
standard cometary constituents, such as H$_2$O, CO$_2$, CO, and dust are best
probed via optical or infrared observations, we predict strong X-ray emission
generated by charge exchange with extended comae of H$_2$ and N$_2$ -- species
which lack strong infrared fluorescence transitions. We find that XMM-Newton
would have been sensitive to charge exchange emission from 1I/`Oumuamua during
the object's close approach to Earth, and that constraints on composition may
have been feasible. We argue for follow-up X-ray observations of newly
discovered ISOs with close-in perihelia. Compositional constraints on the
general ISO population could reconcile the apparently self-conflicting nature
of 1I/`Oumuamua, and provide insight into the earliest stages of planet
formation in extrasolar systems.
