In experiments on resonant tunneling through a "quantum antidot" (a potential hill) in the quantum Hall (QH) regime, periodic conductance peaks were observed as a function of both magnetic field and back gate voltage. A combination of the two periods constitutes a measurement of the charge of the tunneling particles and implies that charge deficiency on the antidot is quantized in units of the charge of quasi-particles of the surrounding QH condensate. The experimentally determined value of the electron charge e is 1.57 x 10(-19) coulomb = (0.98 +/- 0.03)e for the states nu = 1 and nu = 2 of the integer QH effect, and the quasi-particle charge is 5.20 x 10(-20) coulomb = (0.325 +/- 0.01)e for the state nu = 1/3 of the fractional QH effect.