Coronaviruses are responsible for multiple pandemics and millions of deaths globally, including the current pandemic of coronavirus disease 2019 (COVID-19). Development of antivirals against coronaviruses, including the severe acute respiratory syndrome-coronavirus 2 (SARS-CoV-2) responsible for COVID-19, is essential for containing the current and future coronavirus outbreaks. SARS-CoV-2 proteases represent important targets for the development of antivirals because of their role in the processing of viral polyproteins. 3-Chymotrypsin-like protease (3CLpro) is one such protease. The cleavage of SARS-CoV-2 polyproteins by 3CLpro is facilitated by a Cys145-His41 catalytic dyad. We here characterized the catalytic roles of the cysteine-histidine pair for improved understanding of the 3CLpro reaction mechanism, to inform the development of more effective antivirals against Sars-CoV-2. The catalytic dyad residues were substituted by site-directed mutagenesis. All substitutions tested (H41A, H41D, H41E, C145A, and C145S) resulted in a complete inactivation of 3CLpro, even when amino acids with a similar catalytic function to that of the original residues were used. The integrity of the structural fold of enzyme variants was investigated by circular dichroism spectroscopy to test if the catalytic inactivation of 3CLpro was caused by gross changes in the enzyme secondary structure. C145A, but not the other substitutions, shifted the oligomeric state of the enzyme from dimeric to a higher oligomeric state. Finally, the thermodynamic stability of 3CLpro H41A, H41D, and C145S variants was reduced relative the wild-type enzyme, with a similar stability of the H41E and C145A variants. Collectively, the above observations confirm the roles of His41 and Cys145 in the catalytic activity and the overall conformational fold of 3CLpro SARS-CoV-2. We conclude that the cysteine-histidine pair should be targeted for inhibition of 3CLpro and development of antiviral against COVID-19 and coronaviruses.