We present the discovery and early evolution of ASASSN-19bt, a tidal disruption event (TDE) discovered by the All-Sky Automated Survey for Supernovae (ASAS-SN) at a distance of d~115Mpc and the first TDE to be detected by TESS. As the TDE is located in the TESS Continuous Viewing Zone, our data set includes 30 minute cadence observations starting on 2018 July 25, and we precisely measure that the TDE begins to brighten ~8.3 days before its discovery. Our data set also includes 18 epochs of Swift UVOT and XRT observations, 2 epochs of XMM-Newton observations, 13 spectroscopic observations, and ground data from the Las Cumbres Observatory telescope network, spanning from 32 days before peak through 37 days after peak. ASASSN-19bt thus has the most detailed pre-peak data set for any TDE. The TESS light curve indicates that the transient began to brighten on 2019 January 21.6 and that for the first 15 days, its rise was consistent with a flux {propto}t^2^ power-law model. The optical/UV emission is well fit by a blackbody spectral energy distribution, and ASASSN-19bt exhibits an early spike in its luminosity and temperature roughly 32 rest-frame days before peak and spanning up to 14 days, which has not been seen in other TDEs, possibly because UV observations were not triggered early enough to detect it. It peaked on 2019 March 4.9 at a luminosity of L~1.3x10^44^erg/s and radiated E~3.2x10^50^erg during the 41 day rise to peak. X-ray observations after peak indicate a softening of the hard X-ray emission prior to peak, reminiscent of the hard/soft states in X-ray binaries.