We present a radio-quiet quasar at z = 0.237 discovered "turning on" by the intermediate Palomar Transient Factory (iPTF). The transient, iPTF 16bco, was detected by iPTF in the nucleus of a galaxy with an archival Sloan Digital Sky Survey spectrum with weak narrow-line emission characteristic of a low-ionization nuclear emission-line region (LINER). Our follow-up spectra show the dramatic appearance of broad Balmer lines and a power-law continuum characteristic of a luminous ( Lbol ≈ 1045 erg s-1) type 1 quasar 12 yr later. Our photometric monitoring with PTF from 2009-2012 and serendipitous X-ray observations from the XMM-Newton Slew Survey in 2011 and 2015 constrain the change of state to have occurred less than 500 days before the iPTF detection. An enhanced broad Hα/[O iii] λ5007 line ratio in the type 1 state relative to other changing-look quasars also is suggestive of the most rapid change of state yet observed in a quasar. We argue that the >10 increase in Eddington ratio inferred from the brightening in UV and X-ray continuum flux is more likely due to an intrinsic change in the accretion rate of a preexisting accretion disk than an external mechanism such as variable obscuration, microlensing, or the tidal disruption of a star. However, further monitoring will be helpful in better constraining the mechanism driving this change of state. The rapid "turn-on" of the quasar is much shorter than the viscous infall timescale of an accretion disk and requires a disk instability that can develop around a ∼ 108 M⊙ black hole on timescales less than 1 yr.