The 44Ti(t1/2=59 yr) nuclide, an important signature of supernova nucleosynthesis, has recently been observed as live radioactivity by gamma-ray astronomy from the Cas A remnant. We investigate in the laboratory the major 44Ti production reaction 40Ca(alpha, gamma)44Ti (Ec.m. approximately 0.6-1.2 MeV/u by direct off-line counting of 44Ti nuclei. The yield, significantly higher than inferred from previous experiments, is analyzed in terms of a statistical model using microscopic nuclear inputs. The associated stellar rate has important astrophysical consequences, increasing the calculated supernova 44Ti yield by a factor approximately 2 over previous estimates and bringing it closer to Cas A observations.