We report the detection of a peculiar molecular cloud, CO 0.02-0.02, lying about 5' Galactic east from the center of the Galaxy. 12CO images taken with Nobeyama Radio Observatory (NRO) 45 m telescope showed that it is relatively compact (~3×4 pc2) as well as having a very large velocity width (ΔV≥100 km s-1). The cloud has a virial mass about 1 order of magnitude larger than the LTE mass, 9×104 Mʘ, indicating the cloud is apparently gravitationally unbound. New observations with the James Clerk Maxwell Telescope 15 m and the NRO 45 m telescopes show that CO 0.02-0.02 is very bright in the CO (J=3-2) and in the HCN and HCO+ (J=1-0) lines. It appears that the environment may have an unusually high density and temperature, which may be related to the very broad CO line width. We propose that CO 0.02-0.02 may have been accelerated, heated, and compressed in a series of supernovae shocks that have occurred within the last (3-5)×104 yr.