Acetic sulfuric anhydride, CH3COOSO2OH, was produced by the reaction of SO3 and CH3COOH in a supersonic jet. Four isotopologues were observed by microwave spectroscopy. Spectra of both A and E internal rotor states were observed and analyzed, yielding a value of 241.093(30) cm-1 for the methyl group internal rotation barrier of the parent species. Similar values were obtained for the other isotopologues studied. M06-2X/6-311++G(3df,3pd) calculations indicate that the formation of the anhydride proceeds via a π2 + π2 + σ2 cycloaddition reaction within the CH3COOH-SO3 complex. The equilibrium orientation of the methyl group relative to the O-C-C plane is different in the anhydride and in the CH3COOH-SO3 complex, indicating that the -CH3 internal rotation accompanies the cycloaddition reaction. The energies of key points on the potential energy surface were calculated using CCSD(T)/complete basis set with double and triple extrapolation [CBS/(D-T)], and the transformation from the CH3COOH-SO3 complex to CH3COOSO2OH is shown to be nearly barrierless regardless of the orientation of the methyl group. This study provides the second experimental observation of the reaction between a carboxylic acid and SO3 to form a carboxylic sulfuric anhydride in the gas phase. Possible connections to atmospheric aerosol formation are discussed.