  Single stars in ancient globular clusters (GCs) are believed incapable of
producing planetary nebulae (PNe), because their post-asymptotic-giant-branch
evolutionary timescales are slower than the dissipation timescales for PNe.
Nevertheless, four PNe are known in Galactic GCs. Their existence likely
requires more exotic evolutionary channels, including stellar mergers and
common-envelope binary interactions. I carried out a snapshot imaging search
with the Hubble Space Telescope (HST) for PNe in bright Local Group GCs outside
the Milky Way. I used a filter covering the 5007 A nebular emission line of [O
III], and another one in the nearby continuum, to image 66 GCs. Inclusion of
archival HST frames brought the total number of extragalactic GCs imaged at
5007 A to 75, whose total luminosity slightly exceeds that of the entire
Galactic GC system. I found no convincing PNe in these clusters, aside from one
PN in a young M31 cluster misclassified as a GC, and two PNe at such large
angular separations from an M31 GC that membership is doubtful. In a
ground-based spectroscopic survey of 274 old GCs in M31, Jacoby et al. (2013)
found three candidate PNe. My HST images of one of them suggest that the [O
III] emission actually arises from ambient interstellar medium rather than a
PN; for the other two candidates, there are broad-band archival UV HST images
that show bright, blue point sources that are probably the PNe. In a literature
search, I also identified five further PN candidates lying near old GCs in M31,
for which follow-up observations are necessary to confirm their membership. The
rates of incidence of PNe are similar, and small but non-zero, throughout the
GCs of the Local Group.
