We report optimized crystal growth conditions for the quaternary compound CuCrP2S6 by chemical vapor transport. Compositional and structural characterization of the obtained crystals were carried out by means of energy-dispersive x-ray spectroscopy and powder x-ray diffraction. CuCrP2S6 is structurally closely related to the M2P2S6 family (M: transition metal), which contains several compounds that are under investigation as 2D magnets. As-grown crystals exhibit a platelike, layered morphology as well as a hexagonal habitus. We present successful exfoliation of such as-grown crystals down to thicknesses of 2.6 nm corresponding to four layers. CuCrP2S6 crystallizes in the monoclinic space group C2/c. Magnetization measurements reveal an antiferromagnetic ground state with TN≈30 K and a positive Curie-Weiss temperature in agreement with dominant ferromagnetic intralayer coupling. Specific heat measurements confirm this magnetic phase transition and the magnetic order is suppressed in an external magnetic field of about 6 T (8 T) applied parallel (perpendicular) to the ab plane. At higher temperatures between 140-200 K, additional broad anomalies associated with structural changes accompanying antiferroelectric ordering are detected in our specific heat studies.