We report the discovery and follow-up observations of VT 1137-0337: an unusual radio transient found in our systematic search for extragalactic explosions in the VLA Sky Survey (VLASS). VT 1137-0337 is located in the brightest region of a dwarf starburst galaxy at a luminosity distance of 121.6 Mpc. Its 3 GHz luminosity is comparable to luminous radio supernovae associated with dense circumstellar interaction and relativistic outflows. However, its broadband radio spectrum -proportional to Ξ½ β0.35 over a range of 10Γ in frequency and fading at a rate of 5% per year -cannot be directly explained by the shock of a stellar explosion. Jets launched by various classes of accreting black holes also struggle to account for VT 1137-0337's combination of observational properties. Instead, we propose that VT 1137-0337 is a decades old pulsar wind nebula that has recently emerged from within the free-free opacity of its surrounding supernova ejecta. If the nebula is powered by spindown, the central neutron star should have a surface dipole field of βΌ 10 13 β 10 14 G and a present-day spin period of βΌ 10 β 100 ms. Alternatively, the nebula may be powered by the release of magnetic energy from a magnetar. Magnetar nebulae have been proposed to explain the persistent radio sources associated with the repeating fast radio bursts FRB 121102 and FRB 190520B. These FRB persistent sources have not previously been observed as transients, but do bear a striking resemblance to VT 1137-0337 in their radio luminosity, spectral index, and host galaxy properties.