Many of the tools for manipulating the motion of neutral atoms and molecules take their inspiration from techniques developed for charged particles. Traps for atoms-akin to the Paul trap for ions-have paved the way for many exciting experiments, ranging from ultra-precise clocks to creating quantum degenerate matter. Surprisingly, little attention has been paid to developing a neutral particle analogue of a synchrotron-arguably, the most celebrated tool of the charged-particle physicist. So far, the few experiments dealing with ring structures for neutral particles have used cylindrically symmetric designs; in these rings, no force is applied to the particles along the longitudinal direction and the stored particles are free to fill the entire ring. Here, we demonstrate a synchrotron for neutral polar molecules. A packet of ammonia molecules is accelerated, decelerated and focused along the longitudinal direction ('bunched') using the fringe fields between the two halves of a segmented hexapole ring. The stored bunch of cold molecules (T = 0.5 mK) is confined to a 3 mm packet even after a flight distance of over 30 m (40 round trips). Furthermore, we show the injection of multiple packets into the ring.