What is the vacuum chamber made of? Glass, plastic? If so, how about inductively coupling? Power supply on the outside, then inductively couple through the chamber wall. I've done a chamber using a stainless steel cooking pot with glass lid. Seems feasible to me to epoxy a coil on outside of glass lid, with secondary inside lid. Simple circuit to rectify and supply DC inside the chamber with no batteries.
It sounds like you are doing data collection, so implies a micro-controller inside. If so, then get a little Bluetooth board and wirelessly transmit the information collected to an external (to the vacuum chamber) display. Only have solid state electronics inside the vacuum chamber.
Ozwolf