We report the discovery of one newly confirmed planet (P = 66.06 days, R sub(P) = 2.68 + or - 0.17 R sub(+ in circle)) and mass determinations of two previously validated Kepler planets, Kepler-289 b (P = 34.55 days, R sub(P) = 2.15 + or - 0.10 R sub(+ in circle)) and Kepler-289-c (P = 125.85 days, R sub(P) = 11.59 + or - 0.10 R sub(+ in circle)), 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 sub(*) = 1.08 + or - 0.02 M sub(middot in circle), R sub(*) = 1.00 + or - 0.02 R sub(middot in circle), and T sub(eff) = 5990 + or - 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 + or - 6.8 M sub(+ in circle), 4.0 + or - 0.9 M sub(+ in circle), and M = 132 + or - 17 M sub(+ in circle), which we designate PH3 b, c, and d, respectively. Furthermore, the middle planet, PH3 c, has a relatively low density, rho = 1.2 + or - 0.3 g cm super(-3) for a planet of its mass, requiring a substantial H/He atmosphere of 2.1 sub(+0.8) super(-0.3)% by mass, and joins a growing population of low-mass, low-density planets.