One of the stranger planetary rings is Saturn's narrow, clumpy F ring, lying just outside the main rings, in a region disturbed by chaotic orbital dynamics. We show that the F ring has a stable "true core" that dominates its mass and is confined into discontinuous short arcs of particles larger than a few millimeters in radius. The more obvious micron-size particles seen in images, outlining and obscuring the true core, contribute only a small fraction of its mass. We found that these arcs of large particles orbit Saturn in a specific corotational resonance with the nearby 100-kilometer diameter ringmoon Prometheus, which stabilizes the F ring material and allows it to persist within the disturbed region for decades or longer. Toward the end of the observing period, a small chaotic glitch in the orbit of Prometheus temporarily disrupted the confinement, but the arcs seem to be able to adapt.