Data from the high-resolution gamma-ray spectroscopy experiment on HEAO 3 have been searched for line emission from the decay of Ti-44 created in recent, as yet unobserved, Galactic supernova explosions, where the ages and locations are unknown. Because the 78 yr mean life of Ti-44 is comparable to the average time between Galactic supernovae, the gamma-ray line emission from its decay should appear as Galactic point sources. No evidence was found for such emission from a point source anywhere in the Galactic plane, with a 1-sigma-limit of 8.3 x 10(-5) photons cm-2 s-1. Detailed models were developed to simulate the Galactic gamma-ray emission from the decay of Ti-44 produced in both Type I and Type II supernovae. These models were used with the measured gamma-ray line limits to constrain the supernova yields and recurrence periods.