Using a sample of 3.3 x 10(6) B-meson decays collected with the CLEO detector at the Cornell Electron Storage Ring, we have studied B- --> D(0)l(-)<(nu)over bar> and (B) over bar(0) --> D(+)l(-)<(nu)over bar> decays, where l(-) can be either e(-) or mu(-). We distinguish B --> Dl nu from other B semileptonic decays by examining the net momentum and energy of the particles recoiling against D - l pairs. We find Gamma(B --> Dl nu) = (14.1 +/- 1.0 +/- 1.2) ns(-1) and derive branching fractions for B- --> D(0)l(-)<(nu)over bar> and (B) over bar(0) --> D(+)l(-)<(nu)over bar> of (2.32 +/- 0.17 +/- 0.20)% and (2.20 +/- 0.16 +/- 0.19)%, respectively, where the uncertainties are statistical and systematic. We also investigate the B --> Dl nu form factor and the implication of the result for \V-cb\.