The article contains the research results of obtaining a ferroalloy from a carbon ferrochrome dust containing 30,2% of Сr2O3, 23.4% of SiO2, 32.7% of MgO, 5.0% of FeO, 1.6% of CaO, 4.5%of Al2O3, 2.3%of C, and 0.3 %-others. The studies were carried out by a thermodynamic modeling method using the HSC-5.1 software package (Outokumpy) based on the principle of the Gibbs energy minimum, the Box-Hunter rototable planning technique and electric melting of the dust in an arc furnace. It was found that the interaction of the dust with carbon under equilibrium conditions and in the presence of iron leads to formation of Cr4C(T>10000C),Cr3C2, Cr7C3,Cr (T>11000C), FeSi (T>13000C), SiC (T>14000C), SiOg and Si(T>15000C). In the temperature range of 1745-19000C and in the presence of 18-34% of carbon and 8% of iron of the dust mass, the resulting ferroalloy contained 18.5-25.2% of Si and 46.8-49.4% of Cr (in this case the silicon extraction degree into the alloy was 60.0-64.4%, the chromium one–99.8%). When the electrosmelting the granulated dust together with coke and steel shavings, the chromium extraction degree into the alloy was 98-99%, the silicon one–53-57%; the obtained ferroalloys containing 18.3-21.9% of silicon and 45.6-53.6%of chromium meet the requirements to FeCrSi23-grade ferrosilicochromium.