| Summary: | We report the discovery of one newly confirmed planet (P = 66.06 days, R [subscript P] = 2.68 ± 0.17 R [subscript ⊕]) and mass determinations of two previously validated Kepler planets, Kepler-289 b (P = 34.55 days, R [subscript P] = 2.15 ± 0.10 R [subscript ⊕]) and Kepler-289-c (P = 125.85 days, R [subscript P] = 11.59 ± 0.10 R [subscript ⊕]), through their transit timing variations (TTVs). We also exclude the possibility that these three planets reside in a 1:2:4 Laplace resonance. The outer planet has very deep (~1.3%), high signal-to-noise transits, which puts extremely tight constraints on its host star's stellar properties via Kepler's Third Law. The star PH3 is a young (~1 Gyr as determined by isochrones and gyrochronology), Sun-like star with M [subscript *] = 1.08 ± 0.02 M [subscript ☉], R [subscript *] = 1.00 ± 0.02 R [subscript ☉], and T [subscript eff] = 5990 ± 38 K. The middle planet's large TTV amplitude (~5 hr) resulted either in non-detections or inaccurate detections in previous searches. A strong chopping signal, a shorter period sinusoid in the TTVs, allows us to break the mass-eccentricity degeneracy and uniquely determine the masses of the inner, middle, and outer planets to be M = 7.3 ± 6.8 M [subscript ⊕], 4.0 ± 0.9M [subscript ⊕], and M = 132 ± 17 M [subscript ⊕], which we designate PH3 b, c, and d, respectively. Furthermore, the middle planet, PH3 c, has a relatively low density, ρ = 1.2 ± 0.3 g cm[superscript –3] for a planet of its mass, requiring a substantial H/He atmosphere of 2.1[+0.8 over -0.3]% by mass, and joins a growing population of low-mass, low-density planets.
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