Gamma-rays from radioactive 26Al (half-life ~7.2 × 105years) provide a `snapshot' view of continuing nucleosynthesis in the Galaxy. The Galaxy is relatively transparent to such γ-rays, and emission has been found concentrated along its plane. This led to the conclusion that massive stars throughout the Galaxy dominate the production of 26Al. On the other hand, meteoritic data show evidence for locally produced 26Al, perhaps from spallation reactions in the protosolar disk. Furthermore, prominent γ-ray emission from the Cygnus region suggests that a substantial fraction of Galactic 26Al could originate in localized star-forming regions. Here we report high spectral resolution measurements of 26Al emission at 1808.65keV, which demonstrate that the 26Al source regions corotate with the Galaxy, supporting its Galaxy-wide origin. We determine a present-day equilibrium mass of 2.8 (+/- 0.8) solar masses of 26Al. We use this to determine that the frequency of core collapse (that is, type Ib/c and type II) supernovae is 1.9(+/- 1.1) events per century.