Summary form only given. An electron-beam diagnostic has been used to measure electric fields in a capacitively coupled RF discharge in argon. The technique employed achieves a temporal resolution of 5 ns and a spatial resolution of 3 mm. This has proved adequate to measure fields in discharges from 2 mtorr to a few tens of millitorr, RF voltage amplitudes of 100 V to 600 V, and RF driving frequencies up to 13.56 MHz. In 2.3-mtorr discharges at 13.6 MHz, the following have been observed: (1) fields in the plasma of up to 5 V/cm peak-to-peak, (2) asymmetric collapse and expansion of a constant electric field boundary in the sheath, (3) electric field near the powered electrode pointing near the zero in the sheath voltage, and (4) appearance of a double layer in the sheath during its collapse