  The Extragalactic Lens VLBI Imaging Survey (ELVIS) searches for central
images of lensed radio quasars, in order to measure the central density
profiles of distant galaxies. Here we present sensitive multi-epoch Very Long
Baseline Array (VLBA) observations of PMN J1838-3427 at 8 GHz, with a 1 sigma
noise level of 38 microJy beam^(-1). Based on the absence of a central image of
the background source at this level, we explore the possibilities for the
central matter distribution in the lens galaxy. A power-law density profile,
rho ~ r^(-gamma), must have gamma > 1.93. Thus the density profile is close to
an isothermal profile (gamma = 2) or steeper. The upper limit on any
constant-density core in an otherwise isothermal profile is ~< 5 parsecs. We
also derive the constraints on models in which the density profile is
isothermal on kiloparsec scales, but is allowed to have a different power law
in the central ~100 parsecs. If the lens galaxy harbors a supermassive black
hole, the galaxy profile is allowed to be shallower, but for the expected black
hole mass the galaxy profile must still be close to isothermal or steeper.
