We present observations of the first two supernovae discovered with the recently installed Advanced Camera for Surveys (ACS) on the Hubble Space Telescope (HST). The supernovae were found in Wide Field Camera images of the Hubble Deep Field-North taken with the F775W, F850LP, and G800L optical elements as part of the ACS guaranteed time observation program. Spectra extracted from the ACS G800L grism exposures confirm that the objects are Type Ia supernovae (SNe Ia) at redshifts z = 0.47 and 0.95. Follow-up HST observations have been conducted with ACS in F775W and F850LP and with the Near-Infrared Camera and Multi-Object Spectrometer in the near-infrared F110W bandpass, yielding a total of nine flux measurements in the three bandpasses over a period of 50 days in the observed frame. We discuss many of the important issues in doing accurate photometry with the ACS. We analyze the multiband light curves using two different fitting methods to calibrate the supernova luminosities and place them on the SNe Ia Hubble diagram. The resulting distances are consistent with the redshift-distance relation of the accelerating universe model, although evolving intergalactic gray dust remains as a less likely possibility. The relative ease with which these SNe Ia were found, confirmed, and monitored demonstrates the potential ACS holds for revolutionizing the field of high-redshift SNe Ia and therefore of testing the accelerating universe cosmology and constraining the "epoch of deceleration.