An unsaturated fatty acid auxotroph of the oleaginous yeast Apiotrichum curvatum, named UfaM3, blocked in the conversion of stearic to oleic acid was cultivated in single-stage continuous culture. The influence of consumed carbon to nitrogen ratios (C/N ratios, g g−1) obtained at various dilution rates (D) on fatty acid (FA) accumulation and its profiles were studied. In continuous culture in N-limited medium a maximum FA accumulation of 45.6% (g g−1 of dry biomass) was obtained at an optimal D of 0.049 h−1, recording an efficiency of substrate conversion of 0.48 g g−1 and 0.22 g g−1 for biomass and lipids, respectively. The quality of lipid approached cocoa butter at an optimal C/N ratio of between 20 and 30. The C/N ratio in the incoming medium was 38.5 g g−1 with 30 g l−1 of glucose and both C and N sources were completely consumed at a critical D of ≤ 0.07 h−1. The stability of the mutant was demonstrated in the steady-state conditions of the chemostat with regard to the FA composition of its lipids.