We have demonstrated a PET imaging system based on double-sided germanium strip detectors. The demonstration achieved an intrinsic position resolution of 1.35 mm FWHM. This performance was achieved with 2 mm orthogonal strips and a depth sensing capability of 0.5 mm based on timing the pulses at either side of the detector. The system could trigger at energies as low as 15 keV without any image degradation. By selecting events within the 2 keV-wide photopeak, events that scattered within the sampling volume were totally eliminated. If a detector is built with 1 mm strips, the position resolution for PET imaging will not be dominated by the position resolution of the instrument, but by the range of the positron in the sample.