  Inelastic neutron scattering and bulk magnetic susceptibility studies of the
quantum S=1/2 spin ladder system IPA-CuCl3 are performed under hydrostatic
pressure. The pressure dependence of the spin gap $\Delta$ is determined. At
$P=1.5$ GPa it is reduced to $\Delta=0.79$ meV from $\Delta=1.17$ meV at
ambient pressure. The results allow us to predict a soft-mode quantum phase
transition in this system at P$_\mathrm{c}\sim 4$ GPa. The measurements are
complicated by a proximity of a structural phase transition that leads to a
deterioration of the sample.
