We report the discovery of rising X-ray emission from the binary neutron star (BNS) merger event GW170817. This is the first detection of X-ray emission from a gravitational-wave source. Observations acquired with the Chandra X-ray Observatory (CXO) at t ~ 2:3 days post merger reveal no significant emission, with Lx . 3:2x10^38 ergs-1 (isotropic-equivalent). Continued monitoring revealed the presence of an X-ray source that brightened with time, reaching Lx ~ 9x10^39 ergs-1 at t 15:1 days post merger. We interpret these findings in the context of isotropic and collimated relativistic outflows (both on- and off-axis). We find that the broad-band X-ray to radio observations are consistent with emission from a relativistic jet with kinetic energy Ek ~ 10^49-50 erg, viewed off-axis with theta_obs ~ 20-40 degrees. Our models favor a circumbinary density n ~ 10^-4 -10^-2 cm-3, depending on the value of the microphysical parameter epsilon_B = 10^-4 -10^-2. A central-engine origin of the X-ray emission is unlikely. Future X-ray observations at t ~ 100 days, when the target will be observable again with the CXO, will provide additional constraints to solve the model degeneracies and test our predictions. Our inferences on theta_obs are testable with gravitational wave information on GW170817 from Advanced LIGO/Virgo on the binary inclination.