The medium entropy alloy CoCrNi exhibits an exceptional combination of high strength and good ductility at various temperatures. Using atomistic simulations, we have studied the effects of chemical short-range order (CSRO) on quasi-static loading, shock response, crack behavior, and melting in single crystalline and nanocrystalline CoCrNi. It is found that the CSRO is characterized by the local CoCr ordering and Ni segregation. As a result, CoCrNi with CSRO possesses a higher stacking fault energy, a higher yield strength under static loading, a higher twin propensity under static loading, a higher dislocation gliding barrier, a lower dislocation nucleation barrier, a lower twin propensity under shock loading, a lower phase-transformation barrier, a delay of the inverse Hall-Petch effect as the grain size decreases, and a higher melting temperature, compared with random CoCrNi. The underlying physical mechanisms of these findings are discussed.