  We report on the first attempts at searching for CO in red low surface
brightness galaxies, and the first detection of molecular gas in a low surface
brightness (mu_B(0)_{obs} > 23 mag arcsec^{-2}) galaxy. Using the IRAM 30m
telescope, CO(1-0) and CO(2-1) lines were searched for in four galaxies --
P06-1, P05-5, C05-3, & C04-2. In three of the galaxies no CO was detected, to
T_{MB} ~ 1.8mK (at the 3 sigma level). In the fourth galaxy, P06-1, both lines
were detected. Comparing our findings with previous studies shows P06-1 to have
a molecular-to-atomic mass ratio considerably lower than is predicted using
theoretical models based on high surface brightness galaxy studies. This
indicates the N(H_2)/(int{T(CO)dv}) conversion factor for low surface
brightness galaxies may currently be consistently underestimated by a factor of
3 - 20.
