The central 2-degrees x 2-degrees area of the Small Magellanic Cloud has been fully surveyed in the J = 1-->0 rotational transition of (CO)-C-12 at an angular resolution of 8'.8. Most of the emission arises from two large complexes, located in the southwest and northeast regions of the Bar, closely associated with the most intense H I emission from the SMC. Five individual molecular clouds have been identified; their peak antenna temperatures are very weak, approximately 0.035 K. We suggest that for the SMC the conversion factor to derive the column density of molecular hydrogen from the velocity-integrated CO line emission is 6 x 10(21) cm-2 K-1 km-1 s, which is about 20 times higher than the value adopted for our Galaxy. The total mass of molecular gas in the SMC is estimated to be 3 x 10(7) M., implying a ratio of molecular to atomic mass of roughly 7%.