We report the detection of CH$_3$OH emission in comet 46P/Wirtanen on UT 2018 December 8 and 9 using the Atacama Compact Array (ACA), part of the Atacama Large Millimeter/Submillimeter Array (ALMA). These interferometric measurements of CH$_3$OH along with continuum emission from dust probed the inner coma ($<$2000 km from the nucleus) of 46P/Wirtanen approximately one week before its closest approach to Earth ($Delta$ = 0.089 -- 0.092 au), revealing rapidly varying and anisotropic CH$_3$OH outgassing during five separate ACA executions between UT 23:57 December 7 and UT 04:55 December 9, with a clear progression in the spectral line profiles over a timescale of minutes. We present spectrally integrated flux maps, production rates, rotational temperatures, and spectral line profiles of CH$_3$OH during each ACA execution. The variations in CH$_3$OH outgassing are consistent with Wirtanens 9 hr nucleus rotational period derived from optical and millimeter wavelength measurements and thus are likely coupled to the changing illumination of active sites on the nucleus. The consistent blue offset of the line center indicates enhanced CH$_3$OH sublimation from the sunward hemisphere of the comet, perhaps from icy grains. These results demonstrate the exceptional capabilities of the ACA for time-resolved measurements of comets such as 46P/Wirtanen.
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