We report on measurements of the time-dependent CP violating observables in B-s(0) -> D-s(-/+) K--/+ decays using a dataset corresponding to 1.0 fb(-1) of pp collisions recorded with the LHCb detector. We find the CP violating observables C-f = 0.53 +/- 0.25 +/- 0.04, A(f)(Delta Gamma) = 0.37 +/- 0.42 +/- 0.20, A((f) over bar)(Delta Gamma) = 0.20 +/- 0.41 +/- 0.20, S-f = -1.09 +/- 0.33 +/- 0.08, S-(f) over bar = -0.36 +/- 0.34 +/- 0.08, where the uncertainties are statistical and systematic, respectively. Using these observables together with a recent measurement of the B-s(0) mixing phase -2 beta(s) leads to the first extraction of the CKM angle gamma from B-s(0) -> D-s(-/+) K--/+ decays, finding gamma = (115(-43)(+28))degrees modulo 180 degrees at 68% CL, where the error contains both statistical and systematic uncertainties.