A new type of 2-D polarimeter is developed for use in high-resolution observations of solar magnetic fields. Two piezoelastic polarization modulators are used in combination with charge-coupled-device (CCD) image sensors to simultaneously record all four Stokes parameters. Demodulation of the fast 50 and 100 kHz intensity modulations produced by the piezoelastic modulators is achieved by CCD sensors used as synchronous integrators sensitive to a single frequency. The temporary buffer storage needed to separate the charges generated during the two modulation half periods is obtained by covering every second row of the CCD sensors with an opaque mask. The charges are shifted back and forth between the photosensitive uncovered and the adjacent storage rows in phase with the modulation. The polarization signal is calculated from the difference between the charges accumulated in two adjacent rows. A separate CCD sensor is needed for each normalized Stokes parameter Q/I, U/I, or V/I. Because the high modulation frequency lies well above the seeing frequencies occurring in solar observations, precision polarimetry becomes possible. We have demonstrated the capability of this new type of instrument to achieve a polarimetric sensitivity below 10-3 in a single frame. By frame averaging the noise level in the fractional polarization can be reduced to the order of 10-5.