  We report on the results of fifteen months of monitoring the nearby field L1
dwarf WISEP J190648.47+401106.8 (W1906+40) with the Kepler mission. Supporting
observations with the Karl G. Jansky Very Large Array and Gemini North
telescope reveal that the L dwarf is magnetically active, with quiescent radio
and variable H$\alpha$ emission. A preliminary trigonometric parallax shows
that W1906+40 is at a distance of $16.35^{+0.36}_{-0.34}$ pc, and all
observations are consistent with W1906+40 being an old disk star just above the
hydrogen-burning limit. The star shows photometric variability with a period of
8.9 hours and an amplitude of 1.5%, with a consistent phase throughout the
year. We infer a radius of $0.92 \pm 0.07 R_J$ and $\sin i > 0.57$ from the
observed period, luminosity ($10^{-3.67 \pm 0.03} L_\odot$), effective
temperature ($2300 \pm 75$K), and $v \sin i$ ($11.2 \pm 2.2$ km/s). The light
curve may be modeled with a single large, high latitude dark spot. Unlike many
L-type brown dwarfs, there is no evidence of other variations at the $\gtrsim
2%$ level, either non-periodic or transient periodic, that mask the underlying
rotation period. We suggest that the long-lived surface features may be due to
starspots, but the possibility of cloud variations cannot be ruled out without
further multi-wavelength observations. During the Gemini spectroscopy, we
observed the most powerful flare ever seen on an L dwarf, with an estimated
energy of $\sim 1.6 \times 10^{32}$ ergs in white light emission. Using the
Kepler data, we identify similar flares and estimate that white light flares
with optical/ultraviolet energies of $10^{31}$ ergs or more occur on W1906+40
as often as 1-2 times per month.
