We present CO 1-->0 and 2-->1 observations of the dwarf starburst galaxy NG
C 1569 with the IRAM interferometer on Plateau de Bure. We find the CO emis
sion is not spatially associated with the two super star clusters in the ga
laxy, but rather is found in the vicinity of an I-III region. With the reso
lution 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 tran
sition the sizes and linewidths are similar to those of GMCs in the Milky W
ay Galaxy and other nearby systems, with diameters ranging from similar to
40 to 50 pc and linewidths from 4 to 9 km s(-1). The (2-1)/(1-0) line ratio
s range from 0.64 +/- 0.30 to 1.31 +/- 0.60 in the different clouds. The lo
wer line ratios are similar to those seen in typical Galactic GMCs, while v
alues 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 thre
e of the clouds, and we adopt an average value of 6.6 +/- 1.5 times the Gal
actic 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 th
e ISM. Finally, we compare our observations with blue compact dwarf galaxie
s which have been mapped in CO.