We have used the Very Long Baseline Array (VLBA) to image five radio-quiet quasars (RQQs) at milliarcsecond resolution, at frequencies between 1.4 and 5 GHz. These quasars have typical total flux densities of a few millijansky at gigahertz frequencies, and are compact on arcsecond scales. The VLBA images reveal that four of the quasars are dominated by unresolved radio cores, while the fifth has an apparent two-sided jet. Typical core brightness temperatures range from 10^8 K to at least 10^9 K. The compact radio morphologies and X-ray luminosities of many objects in the RQQ sample seem to indicate classical accretion onto black holes as massive as 10^9 solar masses, with emission physics in many ways similar to their radio-loud counterparts. Therefore, the relatively small amount of radiative energy emerging at radio wavelengths in the RQQs may simply be due to the presence of less powerful radio jets.

Accepted for ApJ, Vol. 621, March 1, 2005. 20 pages, 3 figures