Single crystals of CsMnCl3 doped with 0.9% Yb3+ were grown from the melt by the Bridgman technique and studied by means of variable temperature optical spectroscopy. At cryogenic temperatures, near-infrared Yb3+-excitation around 1 mum leads to intense Mn2+ upconversion luminescence in the red spectral region. This very efficient upconversion process is possible because of magnetic Yb3+-Mn2+ exchange interactions, and a new type of upconversion mechanism is found to be active in this system. The upconversion properties of Yb3+:CsMnCl3 are compared to those of Yb3+:RbMnCl3 and Yb3+:CsMnBr3. The upconversion efficiencies at cryogenic temperatures differ by many orders of magnitude. The bridging geometry between Yb3+ and Mn2+ is found to be a key factor for the efficiency of the process. The highest efficiency is observed for the title compound, and this is correlated with the most likely linear Yb3+-Cl--Mn2+ arrangement in this crystal. At 15 K the dominant upconversion mechanism in the title compound involves an energy transfer step. By increasing the temperature to 100 K a new and very efficient mechanism involving a sequence of ground state and excited state absorption steps becomes dominant.