A non - dissipative, implicit, all Mach number algorithm for direct numerical and large eddy simulation of compressible reacting flows, is described. The compressible Navier-Stokes equations are rescaled so that the zero Mach number reacting equations are discretely recovered in the limit of zero Mach number. The dependent variables are co-located in space, and thermodynamic variables are staggered from velocity in time. The algorithm discretely conserves kinetic energy in the incompressible, inviscid, non-reacting limit. The species equations are implicit to allow for stiff chemical mechanisms, and are readily applied to complex chemistry. Numerical examples ranging from one-step chemistry to a nine species, nineteen reaction mechanism for H2 and O2 are presented.