We present microlensing planet OGLE-2017-BLG-0173Lb, with planet-host mass ratio of either q = 2.5 × 10^-5 or q = 6.5 × 10^-5, the lowest or among the lowest ever detected. The planetary perturbation is strongly detected, Δχ 2 ~ 10000, because it arises from a bright (therefore, large) source passing over and enveloping the planetary caustic: a so-called "Hollywood" event. The factor ~2.5 offset in q arises because of a previously unrecognized discrete degeneracy between Hollywood events in which the caustic is fully enveloped and those in which only one flank is enveloped, which we dub "Cannae" and "von Schlieffen," respectively. This degeneracy is "accidental" in that it arises from gaps in the data. Nevertheless, the fact that it appears in a Δχ 2 = 10000 planetary anomaly is striking. We present a simple formalism to estimate the sensitivity of other Hollywood events to planets and show that they can lead to detections close to, but perhaps not quite reaching, the Earth/Sun mass ratio of 3 × 10^-6. This formalism also enables an analytic understanding of the factor ~2.5 offset in q between the Cannae and von Schlieffen solutions. The Bayesian estimates for the host mass, system distance, and planet-host projected separation are M = 0.39^-0.24+0.40, M⊙, DL = 4.8^-1.8+1.5, kpc, and a⊥ = 3. ± 1.6 au, respectively. The two estimates of the planet mass are mp = 3.3^-2.1+3.8, M○ and mp = 8^-6+11, M○. The measured lens-source relative proper motion μ =6 mas yr^-1 will permit imaging of the lens in about 15 years or at first light on adaptive-optics imagers on next-generation telescopes. These will allow one to measure the host mass but probably will not be able to resolve the planet-host mass-ratio degeneracy.