Ofek identified FIRST J141918.9+394036 (hereafter FIRST J1419+3940) as a radio source sharing similar properties and host galaxy type to the compact, persistent radio source associated with the first known repeating fast radio burst, FRB 121102. Law et al. showed that FIRST J1419+3940 is a transient source decaying in brightness over the last few decades. One possible interpretation is that FIRST J1419+3940 is a nearby analog to FRB 121102 and that the radio emission represents a young magnetar nebula (as several scenarios assume for FRB 121102). Another interpretation is that FIRST J1419+3940 is the afterglow of an "orphan" long gamma-ray burst (GRB). The environment is similar to where most such events are produced. To distinguish between these hypotheses, we conducted very long baseline interferometric (VLBI) radio observations using the European VLBI Network (EVN) at 1.6 GHz to spatially resolve the emission and to search for millisecond-duration radio bursts. We detect FIRST J1419+3940 as a compact radio source with a flux density of 620 20 Jy (on 2018 September 18) and a source size of 3.9 0.7 mas (i.e., 1.6 0.3 pc given the angular diameter distance of 83 Mpc). These results confirm that the radio emission is nonthermal and imply an average expansion velocity of (0.10 0.02)c. Contemporaneous high-time-resolution observations using the 100 m Effelsberg telescope detected no millisecond-duration bursts of astrophysical origin. The source properties and lack of short-duration bursts are consistent with a GRB jet expansion, whereas they disfavor a magnetar birth nebula.