Potential energy curves and permanent dipole moments of the (6)Sigma(+) and (8)Sigma(+) ground state of CrX (X = Li, Na, K, Rb and Cs) are calculated by employing the complete active space self-consistent field (CASSCF) and multi-reference configuration interaction (MRCI) methods. The spectroscopic constants for the (6)Sigma(+) and (8)Sigma(+) ground state of these molecules are calculated. Moreover, CrK, CrRb and CrCs molecules with large values of permanent dipole moment (CrK: 5.553 D, CrRb: 6.341 D and CrCs: 6.731 D) at the equilibrium bond distance are potentially interesting candidates for ultracold anisotropic long-range dipole-dipole interactions and many-body physics studies. (C) 2016 Elsevier B.V. All rights reserved.