  We present an exactly solvable model of a Gaussian (flexible) polymer chain
in a quenched random medium. This is the case when the random medium obeys very
long range quadratic correlations. The model is solved in $d$ spatial
dimensions using the replica method, and practically all the physical
properties of the chain can be found. In particular the difference between the
behavior of a chain that is free to move and a chain with one end fixed is
elucidated. The interesting finding is that a chain that is free to move in a
quadratically correlated random potential behaves like a free chain with $R^2
\sim L$, where $R$ is the end to end distance and $L$ is the length of the
chain, whereas for a chain anchored at one end $R^2 \sim L^4$. The exact
results are found to agree with an alternative numerical solution in $d=1$
dimensions. The crossover from long ranged to short ranged correlations of the
disorder is also explored.
