We present a new volume-limited sample of L0-T8 dwarfs out to 25pc defined entirely by parallaxes, using our recent measurements from UKIRT/WFCAM along with Gaia DR2 and literature parallaxes. With 369 members, our sample is the largest parallax-defined volume-limited sample of L and T dwarfs to date, yielding the most precise space densities for such objects. We find the local L0-T8 dwarf population includes 5.5%{+/-}1.2% young objects (<~200Myr) and 2.6%{+/-}1.6% subdwarfs, as expected from recent studies favoring representative ages <~4Gyr for the ultracool field population. This is also the first volume-limited sample to comprehensively map the transition from L to T dwarfs (spectral types ~L8-T4). After removing binaries, we identify a previously unrecognized, statistically significant (>4.4{sigma}) gap ~0.5mag wide in (J-K)_MKO_ colors in the L/T transition, i.e., a lack of such objects in our volume-limited sample, implying a rapid phase of atmospheric evolution. In contrast, the most successful models of the L/T transition to date-the "hybrid" models of Saumon & Marley-predict a pileup of objects at the same colors where we find a deficit, demonstrating the challenge of modeling the atmospheres of cooling brown dwarfs. Our sample illustrates the insights to come from even larger parallax-selected samples from the upcoming Legacy Survey of Space and Time by the Vera Rubin Obsevatory.