Electronic structure calculations in the local spin-density approximation have been carried out on the recently synthesized trimer (CrCl 3 ) 3 exhibiting antiferromagnetic ordering below T N =55 K. The calculated magnetic coupling constant, the paramagnetic Curie temperature, and the decrease of the magnetic moment below T N are well reproduced by the calculations. An interpretation of the spin structure is given that is consistent with all experimental data currently available.