The reactions of muonium atoms with the individual species HO2CCO2H, HO2CCO2-, and -O2CCO2- at similar to 295 K in water have absolute bimolecular rate constants of 5.6, 0.71, and 0.054 x 10(8) M(-1) s(-1), respectively. No such 100-fold pH-dependence has hitherto been seen for muonium, although H and e(aq)(-) also show large pH effects in reactions with oxalic acid. Arrhenius plots for the muonium reactions at pH = 1, 3, and 8 show the unusually small activation energies of less than or equal to 17 kJ/mol for all three acid-base forms of oxalic acid. When the reaction rate of muonium is compared with published data on ordinary H atoms at pH = 1 (57% oxalic acid and 43% hydrogen oxalate ions), one obtains a kinetic isotope effect of 850 favoring muonium. For the dianion at pH greater than or equal to 7, the muonium-to-H rate ratio is >300, These seem to be the largest primary kinetic isotope effects ever reported. The reaction is taken to be addition of muonium to one of the C=O groups, and the large isotope effect and small E(a) suggest considerable contributions from quantum mechanical tunneling.