  We have measured the tunneling between two two-dimensional electron gases at
high magnetic fields $B$, when the carrier densities of the two electron layers
are matched. For filling factors $\nu<1$, there is a gap in the current-voltage
characteristics centered about $V=0$, followed by a tunneling peak at $\sim
6$~mV. Both features have been observed before and have been attributed to
electron-electron interactions within a layer. We have measured high field
tunneling peak positions and fitted gap parameters that are proportional to
$B$, and independent of the carrier densities of the two layers. This suggests
a different origin for the gap to that proposed by current theories, which
predict a $\sqrt{B}$ dependence.
