  (abridged) We investigate the properties of Giant Molecular Clouds (GMCs) in
the molecule-rich galaxy M64 (NGC 4826). In M64, the mean surface density of
molecular gas is 2N(H_2) ~ 10^22 over a 2 kpc region, equal to the surface
densities of individual GMCs in the Milky Way. We observed the J=1->0
transitions of CO, 13CO, and HCN. The line ratio W_CO/W_13CO for 200 pc < R_gal
< 800 pc is comparable to that found in the Milky Way and increases
significantly outside this region, in part due to a large contribution to the
CO emission from diffuse gas, which composes 25% of the molecular mass in the
galaxy. We developed a modified CLUMPFIND algorithm to decompose the 13CO
emission into 25 resolved clouds. The clouds have a luminosity--linewidth
relationship L ~ DV^{2.2+/-0.4}, substantially different from the Milky Way
trend reported by Solomon et al. (1987): L ~ DV^5. Similarly, the clouds have a
linewidth--size relationship of DV ~ R_e^{1.0 +/- 0.3} compared to DV ~ R_e^0.5
in the Milky Way. Estimates of the kinetic and binding energies of the clouds
suggest that the clouds are self-gravitating and significantly overpressured
with respect to the remainder of the ISM in M64. The M64 clouds have a mean
surface density at least 2.5 times larger than observed in Local Group GMCs,
and the surface density is not independent of mass as it is in the Local Group:
\Sigma_H2 ~ M^{0.7+/-0.2}. The clouds are correlated with the recombination
emission from the galaxy, implying that they are star forming; the rate is
comparable to that in other galaxies despite the increased densities of the
clouds. We note that the internal pressures of clouds in several galaxies
scales with the external pressure exerted on the clouds by the ambient ISM:
P_int ~ P_ext^{0.75+/-0.05}.
