We investigate the physical properties and electronic structure upon Cr-doping in the iron arsenide layers of BaFe2As2. This form of hole-doping leads to suppression of the magnetic/structural phase transition in BaFe2-xCrxAs2 for x > 0, but does not lead to superconductivity. For various x values, temperature dependence of the resistivity, specific heat, magnetic susceptibility, Hall coefficient, and single crystal x-ray diffraction data are presented. The materials show signatures of approaching a ferromagnetic state with x, including a metamagnetic transition for x as little as 0.36, an enhanced magnetic susceptibility, and a large Sommerfeld coefficient. Such results reflect renormalization due to spin fluctuations and they are supported by density functional calculations at x = 1. Calculations show a strong interplay between magnetic ordering and chemical ordering of Fe and Cr, with a ferromagnetic ground state. This ferromagnetic ground state is explained in terms of the electronic structure. The resulting phase diagram is suggestive that superconductivity does not derive simply from the suppression of the structural/magnetic transitions.