Do molecular clouds collapse to form stars at the same rate in all environments? In large spiral galaxies, the rate of transformation of H2 into stars (hereafter SFE) varies little. However, the SFE in distant objects (z~1) is much higher than in the large spiral disks that dominate the local universe. Some small local group galaxies share at least some of the characteristics of intermediate-redshift objects, such as size or color. Recent work has suggested that the Star Formation Efficiency (SFE, defined as the SFRate per unit H2) in local Dwarf galaxies may be as high as in the distant objects. A fundamental difficulty in these studies is the independent measure of the H2 mass in metal-deficient environments. At 490 kpc, NGC6822 is an excellent choice for this study; it has been mapped in the CO(2-1) line using the multibeam receiver HERA on the 30 meter IRAM telescope, yielding the largest sample of giant molecular clouds (GMCs) in this galaxy. Despite the much lower metallicity, we find no clear difference in the properties of the GMCs in NGC 6822 and those in the Milky Way except lower CO luminosities for a given mass. Several independent methods indicate that the total H2 mass in NGC 6822 is about 5 x 10^6 Msun in the area we mapped and less than 10^7 Msun in the whole galaxy. This corresponds to a NH2/ICO ~ 4 x 10^{21} cm^-2 /(Kkm/s) over large scales, such as would be observed in distant objects, and half that in individual GMCs. No evidence was found for H2 without CO emission. Our simulations of the radiative transfer in clouds are entirely compatible with these NH2/ICO values. The SFE implied is a factor 5 - 10 higher than what is observed in large local universe spirals.