  The Milky Way Galaxy glows with the soft gamma ray emission resulting from
the annihilation of $\sim 5 \times 10^{43}$ electron-positron pairs every
second. The origin of this vast quantity of antimatter and the peculiar
morphology of the 511keV gamma ray line resulting from this annihilation have
been the subject of debate for almost half a century. Most obvious positron
sources are associated with star forming regions and cannot explain the rate of
positron annihilation in the Galactic bulge, which last saw star formation some
$10\,\mathrm{Gyr}$ ago, or else violate stringent constraints on the positron
injection energy. Radioactive decay of elements formed in core collapse
supernovae (CCSNe) and normal Type Ia supernovae (SNe Ia) could supply
positrons matching the injection energy constraints but the distribution of
such potential sources does not replicate the required morphology. We show that
a single class of peculiar thermonuclear supernova - SN1991bg-like supernovae
(SNe 91bg) - can supply the number and distribution of positrons we see
annihilating in the Galaxy through the decay of $^{44}$Ti synthesised in these
events. Such $^{44}$Ti production simultaneously addresses the observed
abundance of $^{44}$Ca, the $^{44}$Ti decay product, in solar system material.
