We have analyzed high signal-to-noise spectra of the disk galaxy NGC 7217 in order to extract the full line-of-sight velocity distribution along both its major and minor axes. The data reveal that 20%-30% of the stars in this galaxy are in a distinct component on retrograde orbits. This counterrotating population cannot be explained away as a systematic error, and it does not seem to be caused by the bulge's contribution to the velocity distribution. We have developed a new technique for fitting dynamical disk models directly to the galaxy spectra, and application of this method confirms the presence of the distinct counterrotating disk population. NGC 7217 is only the second disk galaxy known to contain counterrotating stars, but we argue that similar components in other regular disk systems would not have been detected by traditional techniques, and so there could exist many such systems. The existence of disk stars on retrograde orbits provides a new clue as to the manner in which the galaxy formed: it favors a scenario in which matter continues to accrete onto the galaxy over a long period of time, with rapid, substantial changes occurring in the angular momentum of the infalling material. The observable consequences of this evolutionary history include a large bulge-to-disk ratio and the absence of strong spiral structure, and so the presence or absnece of a counterrotating component may go some way toward explaining the Hubble sequence for disk galaxies.