We consider adiabatic charge transport through an almost open quantum dot. We show that the charge transmitted in one cycle is quantized in the limit of vanishing temperature and one-electron mean level spacing in the dot. The explicit analytic expression for the pumped charge at finite temperature is obtained for spinless electrons. The pumped charge is produced by both nondissipative and dissipative currents. The former give a quantized contribution to the transferred charge, whereas the latter are responsible for the corrections to charge quantization which are expressed through the conductance of the system.