Rapid radio intra-day variability (IDV) has been discovered in the southern quasar PKS 1257-326. Flux density changes of up to 40% in as little as 45 minutes have been observed in this source, making it, along with PKS 0405-385 and J1819+3845, one of the three most rapid IDV sources known. We have monitored the IDV in this source with the Australia Telescope Compact Array (ATCA) at 4.8 and 8.6 GHz over the course of the last year, and find a clear annual cycle in the characteristic time-scale of variability. This annual cycle demonstrates unequivocally that interstellar scintillation is the cause of the rapid IDV at radio wavelengths observed in this source. We use the observed annual cycle to constrain the velocity of the scattering material, and the angular size of the scintillating component of PKS 1257-326. We observe a time delay, which also shows an annual cycle, between the similar variability patterns at the two frequencies. We suggest that this is caused by a small (~10 microarcsecond) offset between the centroids of the 4.8 and 8.6 GHz components, and may be due to opacity effects in the source. The statistical properties of the observed scintillation thus enable us to resolve source structure on a scale of ~10 microarcseconds, resolution orders of magnitude higher than current VLBI techniques allow. General implications of scintillation for the physical properties of sources and the turbulent ISM are discussed.