In this analysis the decay B- --> D*° e- nu is measured. The underlying data sample consists of about 226 million B-meson pairs accumulated on the Y(4S) resonance by the BABAR detector at the asymmetric e+e- collider PEP II. The reconstruction of the decay uses the channels D*° --> D° pi°, D° --> K- pi+ and pi° --> gamma gamma. The neutrino is not reconstructed. Since the rest frame of the B meson is unknown, the boost w of the D*° meson in the B meson rest frame is estimated by w'. The w' spectrum of the data is described in terms of the partial decay width dGamma/dw given by theory and the detector simulation translating each spectrum dGamma/dw into an expectation of the measured w' spectrum. dGamma/dw depends on a form factor F(w) parameterizing the strong interaction in the decay process. To find the best descriptive dGamma/dw a fit to the data determines the following two parameters of dGamma/dw: (i) F(1)|Vcb|, the product between F at zero D*°-recoil and the Quark mixing parameter |Vcb|; (ii) rho^2, a parameter of the form factor F(w). The former parameter scales the height of dGamma/dw and rho^2 varies the shape of it. The determined values of F(1)|Vcb|, rho^2 and the branching fraction BF(B- --> D*° e- nu) are F(1)|Vcb| = (35.8 +- 0.5 +- 1.5) x 10e-03, rho^2 = (1.08 +- 0.05 +- 0.09) and BF(B- --> D*° e- nu) = (5.60 +- 0.08 +- 0.42)%, where the uncertainties are statistical and systematic, respectively. The value of BF(B- --> D*° e- nu) has been determined by an integration of dGamma/dw over the allowed w range using the fitted values of F(1)|Vcb| and rho^2.