The CrB+ cation molecular system has been investigated with the help of semi-quantitative basis sets [(7s6p4d3f )(Cr)/(4s3p2d1f )(B)] and highly correlated (valence) multi-reference wave functions. Out of a possible manifold of 70 states correlating to the Cr+(S-6, D-6, D-4, (4)G)+B(P-2) atomic states, we have explored a total of 35 states spanning an energy range of about 3.4 eV. The ground state is of X (7)Sigma(+) symmetry with a binding energy of 28.8 kcal/mol at an internuclear distance of 2.242 Angstrom. The next three excited states 1 (5)Sigma(+), 2 (5)Pi, and 3(7)Pi with energy splittings 7.1, 12.9, and 24.3 kcal/mol from the X state, have binding energies of 21.8, 16.5, and 5.1 kcal/mol, respectively. For practically all states we report potential energy curves, total energies, the most common spectroscopic parameters, while we discuss the binding modes using simple chemical diagrams based on valence-bond concepts.