The nearby irregular galaxy Holmberg II (Ho II, DDO 50) has been extensivel
y mapped in H I using the Very Large Array, revealing intricate structure i
n its interstellar gas component, as reported by Puche et al. in 1992. An a
nalysis of these structures shows the neutral gas to contain a number of ex
panding H I holes. The formation of the H I holes has been attributed to mu
ltiple supernova (SN) events occurring within wind-blown shells around youn
g, massive star clusters, with as many as 10-200 SNe required to produce ma
ny of the holes. From the sizes and expansion velocities of the holes, Puch
e et al. assigned ages of similar to 10(7) to 10(8) years. If the SN scenar
io for the formation of the H I holes is correct, it implies the existence
of star clusters with a substantial population of late B, A, and F main-seq
uence stars at the centers of the holes. Many of these clusters should be d
etectable in deep ground-based CCD images of the galaxy. To test the SN hyp
othesis for the formation of the H I holes, we have obtained and analyzed d
eep broadband BVR and narrowband H alpha images of Ho II. We compare the op
tical and H I data and search for evidence of the expected star clusters in
and around the H I holes. We also use the H I data to constrain models of
the expected remnant stellar population. Assuming that the H I holes are cr
eated by multiple SNe, that the number of SNe required can be determined fr
om the observed energetics of the holes, and that the SNe represent the hig
h-mass population of a cluster with a normal initial mass function, we show
that in several of the holes the observed upper limits for the remnant clu
ster brightness are strongly inconsistent with the SN hypothesis described
by Puche et al. Moreover, many of the H I holes are located in regions of v
ery low optical surface brightness that show no indication of recent star f
ormation. Here we present our findings, discuss their implications, and exp
lore possible alternative explanations for the existence of the H I holes i
n Ho II, including the recent suggestion that some of the holes could be pr
oduced by gamma-ray burst events.