  Using star formation histories derived from optically resolved stellar
populations in nineteen nearby starburst dwarf galaxies observed with the
Hubble Space Telescope, we measure the stellar mass surface densities of stars
newly formed in the bursts. By assuming a star formation efficiency (SFE), we
then calculate the inferred gas surface densities present at the onset of the
starbursts. Assuming a SFE of 1%, as is often assumed in normal star-forming
galaxies, and assuming that the gas was purely atomic, translates to very high
HI surface densities (~10^2-10^3 Msun pc^-2), which are much higher than have
been observed in dwarf galaxies. This implies either higher values of SFE in
these dwarf starburst galaxies or the presence of significant amounts of H_2 in
dwarfs (or both). Raising the assumed SFEs to 10% or greater (in line with
observations of more massive starbursts associated with merging galaxies),
still results in HI surface densities higher than observed in 10 galaxies.
Thus, these observations appear to require that a significant fraction of the
gas in these dwarf starbursts galaxies was in the molecular form at the onset
of the bursts. Our results imply molecular gas column densities in the range
10^19-10^21 cm^-2 for the sample. In those galaxies where CO observations have
been made, these densities correspond to values of the CO-H_2 conversion factor
(X_CO) in the range >3-80x10^20 cm^-2 (K km s^-1)^-1, or up to 40x greater than
Galactic X_CO values.
