Engineered strains of the oleaginous yeast Yarrowia lipolytica capable of producing greater than 25% eicosapentaenoic acid (EPA, an (ω-3 polyunsaturated fatty acid) in the total oil fraction are described. These strains comprise various chimeric genes expressing heterologous desaturases, elongases and acyltransferases and optionally comprise various native desaturase and acyltransferase knockouts to enable synthesis and high accumulation of EPA. Production host cells are claimed, as are methods for producing EPA within said host cells.