We present the Atacama Large Millimeter/submillimeter Array survey of CO(2-1) emission from the 1/5 solar metallicity, Local Group dwarf galaxy NGC 6822. We achieve high (0buildrel{primeprime}over{.} 9≈ 2 pc) spatial resolution while covering a large area: four 250 pc × 250 pc regions that encompass ˜ 2/3 of NGC 6822's star formation. In these regions, we resolve ˜ 150 compact CO clumps that have small radii (˜2-3 pc), narrow line width (˜ 1 km s-1), and low filling factor across the galaxy. This is consistent with other recent studies of low-metallicity galaxies, but here shown with a 15× larger sample. At parsec scales, CO emission correlates with 8 μ {{m}} emission better than with 24 μ {{m}} emission and anticorrelates with Hα, so that polycyclic aromatic hydrocarbon emission may be an effective tracer of molecular gas at low metallicity. The properties of the CO clumps resemble those of similar-size structures in Galactic clouds except of slightly lower surface brightness and with CO-to-H2 ratio ˜1-2× the Galactic value. The clumps exist inside larger atomic-molecular complexes with masses typical for giant molecular clouds. Using dust to trace H2 for the entire complex, we find the CO-to-H2 ratio to be ˜ 20{--}25× the Galactic value, but with strong dependence on spatial scale and variations between complexes that may track their evolutionary state. The H2-to-H I ratio is low globally and only mildly above unity within the complexes. The ratio of star formation rate to H2 is ˜ 3{--}5× higher in the complexes than in massive disk galaxies, but after accounting for the bias from targeting star-forming regions, we conclude that the global molecular gas depletion time may be as long as in massive disk galaxies.