  A disorder-dependent Gaussian variational approach is applied to the problem
of a $d$ dimensional polymer chain in a random medium (or potential). Two
classes of variational solutions are obtained. For $d<2$, these two classes may
be interpreted as domain and domain wall. The critical exponent $\nu$
describing the polymer width is $\nu={1\over (4-d)}$ (domain solution) or
$\nu={3\over (d+4)}$ (domain wall solution). The domain wall solution is
equivalent to the (full) replica symmetry breaking variational result. For
$d>2$, we find $\nu={1\over 2}$. No evidence of a phase transition is found for
$2< d< 4$: one of the variational solutions suggests that the polymer chain
breaks into Imry-Ma segments, whose probability distribution is calculated. For
$d>4$, the other variational solution undergoes a phase transition, which has
some similarity with B. Derrida's random energy models.
