  NGC 6240 is a luminous infrared galaxy that, based on recent MERLIN and
CHANDRA observations, appears to host a pair of active galactic nuclei. We
present new, multiepoch and multifrequency radio observations of NGC 6240
obtained using the Very Long Baseline Array (VLBA). These observations resolve
out all of the diffuse radio continuum emission related to starburst activity
to reveal three compact sources, two associated with the infrared and X-ray
nuclei: components N1, the northern nucleus, and S, the southern nucleus; and
component S1, a weak point source lying northeast of component S. The radio
continuum properties of N1 and S both resemble those of compact radio sources
in Seyfert nuclei, including an inverted spectrum at low frequencies and high
brightness temperatures. Component N1 further resolves into a 9 pc linear
source, again resembling compact jets in some well-studied Seyfert nuclei. The
inverted radio spectrum is most likely caused by free-free absorption through
foreground plasma with emission measures of order 1E7 cm^(-6) pc, consistent
with the X-ray spectroscopy which infers the presence of a foreground, Compton
thick absorber. Synchrotron self-absorption may also contribute to the flat
spectrum of component S. Component S1 better resembles a luminous radio
supernova such as those detected in Arp 220, although we cannot specifically
rule out the possibility that S1 may be ejected material from the southern
active nucleus. We demonstrate that the light curve of S1 is at least
consistent with current radio supernova models, and, given the high
star-formation rate in the nuclear region and the (possible) proclivity of
infrared merger galaxies to produce luminous RSNe, it is not surprising that
one such supernova is detected serendipitously in the VLBA observations.
