Multiferroic BiFe0.5Cr0.5O3 solid solution epitaxial films were grown by pulsed laser deposition on SrTiO3 (001) substrates with SrRuO3 bottom electrodes. Formation of the metastable composition in the form of high-quality epitaxial films was made possible by a sequential deposition of 0.1 unit cell amounts of BiFeO3 and BiCrO3. The random distribution of Fe and Cr cation results in a linear response of magnetization with varying magnetic field, consistent with a dominant antiferromagnetic order. Polarization measurements at 77.3K reveal ferroelectric hysteresis with a remanent polarization as high as 60±1μC∕cm2 along the pseudocubic [001] direction.