Yellow needles of InCrBr3 are synthesized from molten InBr3 and elemental Cr at 450 degrees C. Its monoclinic crystal structure (a = 412.09(3) pm, b = 1500.6(1) pm, c = 937.65(6) pm, beta = 94.386(6)degrees; P2(1)/c; Z = 4), similar to the NH4CdCl3 type, has been determined by single crystal structure investigations. While the chromium cations are found in Jahn-Teller distorted Br- octahedra, monovalent indium cations are located in strongly distorted trigonal Br- prisms which are tricapped by additional Br- anions. InCrBr3 shows Curie-Weiss paramagnetism and exhibits antiferromagnetic ordering below 12 K. Ab initio band structure calculations reveal that the indium-bromine bonds are weakened due to out-of-phase interactions in the highest occupied bands. Neutron diffraction experiments at 2 K for InCrBr3 and InFeBr3 yield additional reflections because of antiferromagnetic ordering. Both spin structures have been determined and refined on the basis of the Rietveld method.