GRS 1747-312 is a bright transient X-ray source in the globular cluster Terzan 6 with quasi-periodic outbursts approximately every 4.5 months. We carried out 2-60 keV target-of-opportunity observations during eight outbursts with the Proportional Counter Array on the RXTE satellite, for a total exposure time of 301 ks, and detect the first unambiguous thermonuclear X-ray bursts from this source. This identifies the compact accretor in this binary as a neutron star. The neutron star identification implies that twelve out of thirteen luminous (above 1036 erg s-1) X-ray sources in Galactic globular clusters harbor neutron stars, with AC211's nature (in M15) remaining elusive. We observed 24 transitions of eclipses of the X-ray emitting region by the companion star and are able to improve the accuracy of the orbital period by a factor of 104. The period is P=0.514980303(7) d. We do not detect a period derivative with an upper limit of |dot {P}/P|=3*E-8 yr-1. Archival Chandra data were analyzed to further refine the X-ray position, and the cluster's center of gravity was re-determined from optical data resulting in a correction amounting to 2 core radii. We find that GRS 1747-312 is 0.2+/-0.2 core radii from the cluster center.