SN 2008D was discovered while following up an unusually bright X-ray transient in the nearby spiral galaxy NGC 2770. We present early optical spectra (obtained 1.75 days after the X-ray transient) which allowed the first identification of the object as a supernova at redshift z = 0.007. These spectra were acquired during the initial declining phase of the light curve, likely produced in the stellar envelope cooling after shock breakout, and rarely observed. They exhibit a rather flat spectral energy distribution with broad undulations, and a strong, W-shaped feature with minima at 3980 and 4190 AA (rest frame). We also present extensive spectroscopy and photometry of the supernova during the subsequent photospheric phase. Unlike supernovae associated with gamma-ray bursts, SN 2008D displayed prominent He features and is therefore of Type Ib. ; Comment: 7 pages, 5 figures, 2 tables; accepted for publication in ApJL; typos fixed after proofs