  In this paper we give describe a new connection between the dilogarithm
function and solutions to Pell's equation $x^2-ny^2 = \pm 1$. For each solution
$x,y$ to Pell's equation we obtain a dilogarithm identity whose terms are given
by the continued fraction expansion of the associated unit $x+y\sqrt{n} \in
\Z[\sqrt{n}]$. We further show that Ramanujan's dilogarithm value-identities
correspond to an identity for the regular ideal hyperbolic hexagon.
