The first galaxies contain stars born out of gas with little or no metals. The lack of metals is expected to inhibit efficient gas cooling and star formation but this effect has yet to be observed in galaxies with oxygen abundance relative to hydrogen below a tenth of that of the Sun. Extremely metal poor nearby galaxies may be our best local laboratories for studying in detail the conditions that prevailed in low metallicity galaxies at early epochs. Carbon Monoxide (CO) emission is unreliable as tracers of gas at low metallicities, and while dust has been used to trace gas in low-metallicity galaxies, low-spatial resolution in the far-infrared has typically led to large uncertainties. Here we report spatially-resolved infrared observations of two galaxies with oxygen abundances below 10 per cent solar, and show that stars form very inefficiently in seven star-forming clumps of these galaxies. The star formation efficiencies are more than ten times lower than found in normal, metal rich galaxies today, suggesting that star formation may have been very inefficient in the early Universe.