On 2012 May 17.2 UT, only 1.5 +/- 0.2 d after explosion, we discovered SN 2012cg, a Type Ia supernova (SN Ia) in NGC 4424 (d ~ 15 Mpc). As a result of the newly modified strategy employed by the Lick Observatory SN Search, a sequence of filtered images was obtained starting 161 s after discovery. Utilizing recent models describing the interaction of SN ejecta with a companion star, we rule out a ~1 M_Sun companion for half of all viewing angles and a red-giant companion for nearly all orientations. SN 2012cg reached a B-band maximum of 12.09 +/- 0.02 mag on 2012 June 2.0 and took ~17.3 d from explosion to reach this, typical for SNe Ia. Our pre-maximum brightness photometry shows a narrower-than-average B-band light curve for SN 2012cg, though slightly overluminous at maximum brightness and with normal color evolution (including some of the earliest SN Ia filtered photometry ever obtained). Spectral fits to SN 2012cg reveal ions typically found in SNe Ia at early times, with expansion velocities >14,000 km/s at 2.5 d past explosion. Absorption from C II is detected early, as well as high-velocity components of both Si II 6355 Ang. and Ca II. Our last spectrum (13.5 d past explosion) resembles that of the somewhat peculiar SN Ia 1999aa. This suggests that SN 2012cg will have a slower-than-average declining light curve, which may be surprising given the faster-than-average rising light curve.
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