This research evaluated a method of scaling a single element sub-scale combustor to match the combustion instability modes of a full-scale liquid rocket engine. The experiments used a shear-coaxial injector in an atmospheric chamber using gaseous oxygen and a heated gaseous methane/nitrogen fuel mixture. The flow conditions matched the full-scale equivalence ratio, propellant velocities and propellant volumetric flow rates. The first set of experiments empirically determined the effect of chamber diameter on chamber temperature. The results were used to calculate the dimensions of the sub-scaled combustion chamber that would match the transverse frequencies of the full-scale engine. The scaled chamber was used in two sets of experiments. The stationary tests placed the injector at the center of the chamber and 0.25 in. from the wall. The centered test displayed evidence of coupling between the 1L chamber mode and the injector oxygen post at 885 Hz. Injector coupling was also observed during experiments with the full-scale rocket engine. With the injector 0.25 in. from the wall, the average chamber temperature dropped about 350°C from the centered test. As a consequence, the frequencies of the transverse modes were lower than the full-scale values. No major difference was found in this research between the stable and unstable set points of the full-scale engine. A translating stage was used to evaluate where various chamber modes appear as a function of injector location. The results show that the 1L chamber mode is present at every location and transverse modes appear as the injector moves near the wall.