We present new ^12^CO (J=1-0) observations of He 2-10, a blue compact dwarf galaxy about 8.7Mpc away, taken with the Atacama Large Millimeter Array. These are the highest spatial and spectral resolution observations, to date, of the molecular gas in this starburst galaxy. We measure a molecular mass of (1.2+/-0.4)x10^8^M_{sun}_ in He 2-10, and 75% of the molecular gas mass is contained within the northern region of the galaxy near the previously identified young super star clusters, which has a projected size of about 300pc. We use the CPROPS algorithm to identify 119 resolved giant molecular clouds distributed throughout the galaxy, and the molecular gas contained within these clouds makes up between 45% and 70% of the total molecular mass. The molecular clouds in He 2-10 have similar median sizes (~26pc), luminous masses (~4x10^5^M_{sun}_), and surface densities (~180M_{sun}_/pc^2^) to Milky Way clouds. However, He 2-10 clouds have velocity dispersions (~3km/s) about 50% higher than those in the Milky Way. We provide evidence that He 2-10 clouds tend to be in virial equilibrium, with the virial and luminous masses scaling according to M_vir_{propto}M_lum_^1.2+/-0.1^, similar to clouds in the Milky Way. However, we measure a scaling relationship between luminous mass and size, M_lum_{propto}R^3.0+/-0.3^, that is steeper than what is observed in Milky Way clouds. Assuming that He 2-10 molecular clouds are virialized, we infer values of the CO-to-H_2_ conversion factor ranging from 0.5 to 13 times the standard value in the solar neighborhood. Given star formation efficiencies as low as 5%, the most massive molecular clouds in He 2-10 currently have enough mass to form the next generation of super star clusters in the galaxy.