Acidic zeolites catalyze dimethyl ether (DME) carbonylation to methyl acetate at low temperatures (400-450 K) with high selectivity (>99%). Steady-state, transient, and isotopic exchange studies were combined with adsorption-desorption of probe molecules and infrared spectroscopy to identify methyl and acetyl groups as adsorbed species and to propose elementary steps consistent with kinetic and spectroscopic evidence. Carbonylation rates are proportional to CO pressure (up to ~ 1 MPa) and independent of DME pressure; water strongly inhibits rates but does not influence CO and DME kinetic dependences. Carbonylation proceeds via initiation steps that form methyl groups via DME-OH reactions. Subsequent propagation steps involve slow carbonylation of methyl or oxonium ions and fast methylation of the resulting acetyls with DME to re-form methyl groups. These steps avoid the formation of water and its inhibitory effects, prevalent in similar reactions of methanol. Carbonylation rates (per Al) depend strongly on zeolite structure and on the density of acidic OH groups, but not on the number and type of inorganic cations that bind CO.