We present a measurement of the rate of distant Type Ia supernovae derived using 4 large subsets of data from the Supernova Cosmology Project. Within this fiducial sample, which surveyed about 12 square degrees, thirty-eight supernovae were detected at redshifts 0.25--0.85. In a spatially-flat cosmological model consistent with the results obtained by the Supernova Cosmology Project, we derive a rest-frame Type Ia supernova rate at a mean redshift $zsimeq0.55$ of $1.53 {^{+0.28}_{-0.25}} {^{+0.32}_{-0.31}} 10^{-4} h^3 {rm Mpc}^{-3} {rm yr}^{-1}$ or $0.58 {^{+0.10}_{-0.09}} {^{+0.10}_{-0.09}} h^2 {rm SNu}$ (1 SNu = 1 supernova per century per $10^{10}$Lbsun), where the first uncertainty is statistical and the second includes systematic effects. The dependence of the rate on the assumed cosmological parameters is studied and the redshift dependence of the rate per unit comoving volume is contrasted with local estimates in the context of possible cosmic star formation histories and progenitor models.
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