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In circumstellar gas, the complex organic molecule methanol has been foundalmost exclusively around young stellar objects, and is thus regarded as asignpost of recent star formation. Here we report the first probable detectionof methanol around an evolved high-mass star, in the complex circumstellarenvironment around the Luminous Blue Variable $\eta$ Carinae, while using ALMAto investigate molecular cloud conditions traced by CO (2-1) in an orbit phaseof the massive binary preceding the 2020 periastron. Favoring methanol over a$^{13}$CS alternative, the emission originates from hot ($T_{\rm{gas}} \simeq$700 K) material, $\sim$2$''$ (0.02 pc) across, centered on the dust-obscuredbinary in contrast to the CO which traces inner layers of the extended massiveequatorial torus, and is accompanied by prominent absorption in a cooler($T_{\rm{gas}} \simeq$ 110 K) layer of gas. We also report detections of waterin $Herschel$/HIFI observations at 557 GHz and 988 GHz. The methanol abundanceis several to 50 times higher than observed towards several lower mass stars,while water abundances are similar to those observed in cool, dense molecularclouds. The very high methanol:water abundance ratio in the core of $\eta$Carinae may suggest methanol formation processes similar toFischer-Tropsch-type catalytic reactions on dust grains. These observationsprove that complex molecule formation can occur in the chemically evolvedenvironments around massive stars in the end stages of their evolution, givensufficient gas densities and shielding conditions as may occur in materialaround massive interacting companions and merger remnants.

CO, Water, and Possible Methanol in Eta Carinae Approaching Periastron