We present the discovery observations of the optical counterpart of the gamma-ray burst GRB 990712 taken 4.16 hr after the outburst and discuss its light curve observed in the V, R, and I bands during the first similar to 35 days after the outburst. The observed light curves were fitted with a power-law decay for the optical transient (OT), plus an additional component that was treated in two different ways. First, the additional component was assumed to be an underlying galaxy of constant brightness. The resulting slope of the decay is 0.97(-0.02)(+0.05), and the magnitudes of the underlying galaxy are V = 22.3 +/- 0.05, R = 21.75 +/- 0.05, and I = 21.35 +/- 0.05. Second, the additional component was assumed to be a galaxy plus an underlying supernova with a time-variable brightness identical to that of GRB 980425, appropriately scaled to the redshift of GRB 990712. The resulting slope of the decay is similar, but the goodness of fit is worse, which would imply that either this GRB is not associated with an underlying supernova or the underlying supernova is much fainter than the supernova associated with GRB 980425. The galaxy in this case is fainter: V = 22.7 +/- 0.05, R = 22.25 +/- 0.05, and I = 22.15 +/- 0.05, and the OT plus the underlying supernova at a given time is brighter. Measurements of the brightnesses of the OT and the galaxy by late-time Hubble Space Telescope observation and ground-based observations can thus assess the presence of an underlying supernova.