Jointly Gaussian memoryless sources $(y_1,\ldots ,y_N)$ are observed
at $N$ distinct terminals. The goal is to efficiently encode the
observations in a distributed fashion so as to enable reconstruction
of any one of the observations, say $y_1$, at the decoder subject to
a quadratic fidelity criterion. Our main result is a {\em precise} 
characterization of the rate-distortion region when the covariance
matrix of the sources satisfies a ``tree-structure'' condition. In
this situation, a natural analog/digital separation scheme optimally 
trades off the distributed quantization rate tuples and the distortion 
in reconstruction: each encoder consists of a point-to-point vector 
quantizer followed by a Slepian-Wolf binning encoder.