We present CO (1-0) and (2-1) observations of the dwarf starburst galaxy NGC 1569 with the IRAM interferometer on Plateau de Bure. We find the CO emission is not spatially associated with the two super star clusters in the galaxy, but rather is found in the vicinity of an HII region. With the resolution of our data, we can resolve the CO emission into five distinct giant molecular clouds, four are detected at both transitions. In the (1-0) transition the sizes and linewidths are similar to those of GMCs in the Milky Way Galaxy and other nearby systems, with diameters ranging from about 40 to 50 pc and linewidths from 4 to 9 kms. The (2-1)/(1-0) line ratios range from 0.64 +- 0.30 to 1.31 +- 0.60 in the different clouds. The lower line ratios are similar to those seen in typical Galactic GMCs, while values higher than unity are often seen in interacting or starburst galaxies. We use the virial theorem to derive the CO-H(2) conversion factor for three of the clouds, and we adopt an average value of 6.6 +-1.5 times the Galactic conversion factor for NGC 1569 in general. We discuss the role of the molecular gas in NGC 1569, and its relationship to the hot component of the ISM. Finally, we compare our observations with blue compact dwarf galaxies which have been mapped in CO.
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