We report the observation of the decay B- → D(s)((*)+) K- ℓ- ν(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- ν(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- ν(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.