  In previous work it had been shown that the remarkable homogeneous space $M=
\operatorname{Diff}(S^1)/\operatorname{PSL} (2,\Bbb{R})$ sits as a complex
analytic and K\"ahler submanifold of the Universal Teichm\"uller Space. There
is a natural immersion $\Pi$ of $M$ into the infinite-dimensional version (due
to Segal) of the Siegel space of period matrices. That map $\Pi$ is proved to
be injective, equivariant, holomorphic, and K\"ahler-isometric (with respect to
the canonical metrics). Regarding a period mapping as a map describing the
variation of complex structure, we explain why $\Pi$ is an infinite-dimensional
period mapping.
