  By introducing a $\int dt \, g\left(\Tr \Phi^2(t)\right)^2$ term into the
action of the $c=1$ matrix model of two-dimensional quantum gravity, we find a
new critical behavior for random surfaces. The planar limit of the path
integral generates multiple spherical ``bubbles'' which touch one another at
single points. At a special value of $g$, the sum over connected surfaces
behaves as $\Delta^2 \log\Delta$, where $\Delta$ is the cosmological constant
(the sum over surfaces of area $A$ goes as $A^{-3}$). For comparison, in the
conventional $c=1$ model the sum over planar surfaces behaves as $\Delta^2/
\log\Delta$.
