Spectroscopic and theoretical studies concerning thea3II state of CH+ are reviewed, with particular consideration given to the infrared predissociation spectrum of the ion. This spectrum is primarily due to vibration-rotation transitions of thea3II state involvingv=5 to 12 andJ=20 to 35. Some results of a spectral simulation, making use of a rotationally-adiabatic model, are presented to justify the proposed assignment. The nuclear-hyperfine structure of the observed transitions is studied in detail, with a new calculation of splittings presented. Some semi-quantitative conclusions can be drawn with reference to the variation of the Fermi Contact parameter,b, as a function of internuclear distance.