For applications to cryptography, one is interested in constructing curves of genus less than or equal to 3 over finite fields whose Jacobians have complex multiplication. Several algorithms exist in the cases of elliptic curves and genus 2 curves, however, less in known in the genus 3 case. We restrict to the case of Picard curves which are genus 3 curves of the form y^3 = f(x) where f is a separable polynomial of degree 4. We discuss some difficulties encountered in the genus 3 case and present an algorithm to construct Picard curves with complex multiplication using a Chinese Remainder Theorem approach. This is joint work with Kirsten Eisenträger.