PRIMA (instrument for Phase-Referenced Imaging and Microarcsecond Astrometry) is a conceptual study for a single-baseline dual-feed instrument for the Very Large Telescope Interferometer (VLTI), which is under construction by the European Southern Observatory on Cerro Paranal in Chile. The goals of PRIMA include narrow-angle astrometry with a precision of 10 μas over an arc of 10", and imaging of faint sources with the full sensitivity of the 8 m telescopes in the VLT array. Key scientific programs that can be carried out with PRIMA in imaging mode include observations of active galactic nuclei, the Galactic Center, stars, and circumstellar matter. Scientific drivers for the astrometry are searches for planets and low-mass stellar companions, binary stars, dynamics of clusters, and (relative) parallaxes. We list the main performance requirements for PRIMA, present system architectures for the dual-beam system, and discuss limitations of the interferometric field-of-view.