We report the observation of the decay B^- → D_s^((*)+)K^-ℓ^-ν̅ _ℓ based on 342 fb^(-1) of data collected at the Υ(4S) resonance with the BABAR detector at the PEP-II e^+e^- storage rings at SLAC. A simultaneous fit to three D_s^+ decay chains is performed to extract the signal yield from measurements of the squared missing mass in the B meson decay. We observe the decay B^- → D_s^((*)+)K^-ℓ^-ν̅ _ℓ with a significance greater than 5 standard deviations (including systematic uncertainties) and measure its branching fraction to be B(B^- → D_s^((*)+)K^-ℓ^-ν̅ _ℓ)=[6.13_(-1.03)^(+1.04)(stat)±0.43(syst)±0.51(B(D_s))]×10^(-4), where the last error reflects the limited knowledge of the D_s branching fractions
