F1-ATPase is a catalytic portion of the rotary molecular motor, F1Fo-ATP synthase. Cooperative ATP hydrolysis at the three catalytic sites of the F1-ATPase is connected with rotation of the central gamma-subunit inside a cylinder made of three a subunits and three beta subunits. Various experimental works have shown that the gamma-subunit rotates with irregular dwells. A simple kinetic model of this paper explains dwells during rotation as a result of the deterministic chaos. It is shown that the deterministic chaos occurs under the rate constants close to the known experimental estimations. Time duration of dwells in the model are close to those observed experimentally. Our model explains the known irregular occupancy of catalytic sites of F1-ATPase by nucleotides.