The Ce (Formula presented.) Mg (Formula presented.) Co (Formula presented.) system evolves from a Pauli paramagnetic ground state for x = 0 to a ferromagnetic ground state for (Formula presented.) in single-phase, polycrystalline samples [Lamichhane, V. Taufour, A. Palasyuk, Q. Lin, S.L. Budko, and P.C. Canfield, (Formula presented.) : transformation of a Pauli paramagnet into a strong permanent magnet, Phys. Rev. Appl. 9 (2018), p. 024023]. In order to better understand this behaviour, single-crystalline samples of Ce (Formula presented.) Mg (Formula presented.) Co (Formula presented.) for x = 0.01, 0.16, 0.24, 0.35, 0.43 and 0.50 were grown using the flux growth technique, and electrical transport and magnetic properties were studied. The (Formula presented.) -x phase diagram we infer shows that the system has a quantum phase transition near x = 0.35, transforming to a ferromagnetic ground state.