This paper investigates the linear stability of compressible reacting mixing layers with special emphasis on three-dimensionality. The governing equations for laminar flows are from two-dimensional compressible boundary-layer equations. The chemistry is a finite rate single step irreversible reaction with Arrhenius kinetics. For incompressible reacting mixing layers, two-dimensional outer modes are more amplified than three-dimensional ones. For compressible non-reacting mixing layers at $M_c$ > 0.6, the most unstable modes are oblique center modes that are subsonic relative to both free streams. For compressible reacting mixing layers with $T_{ad}$ > 3, the most unstable modes are two-dimensional outer modes even at high Mach numbers. Three-dimensional modes agree well with experimental data compared to two-dimensional modes.