  We present the results of a Hubble Space Telescope Wide Field Camera 3
imaging survey of 11 of the lowest mass brown dwarfs in the Pleiades known
(25-40 Mjup). These objects represent the predecessors to T dwarfs in the
field. Using a semi-empirical binary PSF-fitting technique, we are able to
probe to 0.03" (0.75 pixel), better than 2x the WFC3/UVIS diffraction limit. We
did not find any companions to our targets. From extensive testing of our
PSF-fitting method on simulated binaries, we compute detection limits which
rule out companions to our targets with mass ratios of $q\gtrsim0.7$ and
separations $a\gtrsim4$ AU. Thus, our survey is the first to attain the high
angular resolution needed to resolve brown dwarf binaries in the Pleiades at
separations that are most common in the field population. We constrain the
binary frequency over this range of separation and mass ratio of 24-40 Mjup
Pleiades brown dwarfs to be <11% for 1$\sigma$ (<26% at 2$\sigma$). This binary
frequency is consistent with both younger and older brown dwarfs in this mass
range.
