At q = (1.81+/-0.20)*10^-5, KMT-2018-BLG-0029Lb has the lowest planet-host mass ratio q of any microlensing planet to date by more than a factor of two. Hence, it is the first planet that probes below the apparent "pile-up" at q = 5-10*10^-5. The event was observed by Spitzer, yielding a microlens-parallax pi_E measurement. Combined with a measurement of the Einstein radius theta_E from finite-source effects during the caustic crossings, these measurements imply masses of the host M_host = 1.14 (+0.10, -0.12) M_sun and planet M_planet = 7.59 (+0.75, -0.69) M_Earth, system distance D_L = 3.38 (+0.22, -0.26) kpc and projected separation a_perp = 4.27 (+0.21, -0.23) au. The blended light, which is substantially brighter than the microlensed source, is plausibly due to the lens and could be observed at high resolution immediately.