The pure rotational spectrum of AlCH3 has been recorded using millimeter/submillimeter direct absorption techniques. This is the first time this species has been observed in the laboratory by any spectroscopic method. AlCH3 was created in a d.c. discharge by the reaction of aluminum vapor and dimethyl mercury. The K = 0, 1, 2, and 3 components in fourteen rotational transitions of this symmetric top molecule were measured in the frequency range 188--517 GHz and several lines recorded for K = 4, 5 and 6 ladders as well. From these data, rotational parameters have been accurately determined. This study confirms the structure predicted for AlCH3 from theoretical calculations, as well as provides precise rest frequencies. Aluminum-bearing molecules have been observed in the late-type carbon star IRC +10216, which also has a large abundance of CH4. Hence, AlCH3 may be detectable in this object and perhaps in other sources.