A 10-kHz one-dimensional Rayleigh-CH4 Raman instrument capable of achieving highly precise measurement of temperature and methane mole fraction is demonstrated. The system uses a pulse-burst laser as the light source and back-illuminated electron-multiplied CCD cameras as the detectors. The cameras are operated in the subframe burst gating mode, to combine a high sampling rate, low noise, and a slow readout. The improved precision of this configuration is demonstrated by measuring temperature and methane mole fractions in ambient temperature gas mixtures and in a non-premixed inverse diffusion flame.