In order to understand atmospheric methane (CH$\mathrm{<mrow\; data-mjx-texclass="ORD">4</mrow>}$) biogeochemistry now and in the future, we must apprehend its natural variability, without anthropogenic influence. Samples of ancient air trapped within ice cores provide the means to do this. Here we analyze the ultrahigh-resolution CH$\mathrm{<mrow\; data-mjx-texclass="ORD">4</mrow>}$ record of the West Antarctic Ice Sheet Divide ice core 67.2–9.8 ka and find novel, atmospheric CH$\mathrm{<mrow\; data-mjx-texclass="ORD">4</mrow>}$ variability at centennial time scales throughout the record. This signal is characterized by recurrence intervals within a broad 80–500 year range, but we find that age-scale uncertainties complicate the possible isolation of any periodic frequency. Lower signal amplitudes in the Last Glacial relative to the Holocene may be related to incongruent effects of firn-based signal smoothing processes. Within interstadial and stadial periods, the peak-to-peak signal amplitudes vary in proportion to the underlying millennial-scale oscillations in CH$\mathrm{<mrow\; data-mjx-texclass="ORD">4</mrow>}$ concentration—the relative amplitude change is constant. We propose that the centennial CH$\mathrm{<mrow\; data-mjx-texclass="ORD">4</mrow>}$ signal is related to tropical climate variability that influences predominantly low-latitude wetland CH$\mathrm{<mrow\; data-mjx-texclass="ORD">4</mrow>}$ emissions.