  We present the discovery of a slowly-evolving, extragalactic radio transient,
FIRST J141918.9+394036, identified by comparing a catalog of radio sources in
nearby galaxies against new observations from the Very Large Array Sky Survey.
Analysis of other archival data shows that FIRST J141918.9+394036 faded by a
factor of ~50 over 23 years, from a flux of ~26 mJy at 1.4 GHz in 1993 to an
upper limit of 0.4 mJy at 3 GHz in 2017. FIRST J141918.9+394036 is likely
associated with the small star-forming galaxy SDSS J141918.81+394035.8 at a
redshift z=0.01957 (d=87 Mpc), which implies a peak luminosity $\nu L_\nu
\gtrsim 3\times10^{38}$ erg s$^{-1}$. If interpreted as an isotropic
synchrotron blast wave, the source requires an explosion of kinetic energy
~10^{51} erg some time prior to our first detection in late 1993. This
explosion could plausibly be associated with a long gamma-ray burst (GRB) or
the merger of two neutron stars. Alternatively, FIRST J141918.9+394036 could be
the nebula of a newly-born magnetar. The radio discovery of any of these
phenomena would be unprecedented. Joint consideration of the event light curve,
host galaxy, lack of a counterpart gamma-ray burst, and volumetric rate
suggests that FIRST J141918.9+394036 is the afterglow of an off-axis (`orphan')
long GRB. The long time baseline of this event offers the best available
constraint in afterglow evolution as the bulk of shock-accelerated electrons
become non-relativistic. The proximity, age, and precise localization of FIRST
J141918.9+394036 make it a key object for understanding the aftermath of rare
classes of stellar explosion.
