Seven Q branch transitions between 7.8 and 20 GHz have been observed in the distortion moment pure rotational spectrum of 12CH4 in its ground vibronic state. The spectrum was obtained using a conventional Stark modulated microwave spectrometer specially modified for the detection of very weak lines. From the frequencies of these seven transitions, along with the ortho–para splitting known for the (J = 2) state and two Q branch splittings measured earlier by infrared–microwave double resonance, we have determined the one quartic tensor distortion constant DT, the two sextic constants H4T and H6T, and the three octic constants L4T, L6T, and L8T. These are (in Hz): DT = (132 943.41 ± 0.71); H4T = −(16.9839 ± 0.0076); H6T = (11.0342 ± 0.0086); L4T = (20.27 ± 0.24) × 10−4; L6T = −(26.77 ± 0.35) × 10−4; L8T = −(30.0 ± 1.8) × 10−4. The errors are the standard deviations resulting from a least squares analysis. Estimates are also given of the absolute errors. These results consitute the first measurement of the octic distortion constants. The values for DT, H4T, and H6T are compared to earlier determinations. The theoretical considerations that affect the observation of these transitions are reviewed and a detailed description of the special experimental techniques used is given. The method of analysis is described. Finally, as an aid to other high resolution studies of methane and to possible astrophysical detection of the molecule, the Q branch splittings are tabulated up to J = 21.