I bet people do, but it's probably not advisable !
For one thing - plasmas like the VT50 can get quite warm and require cooling with fans. If you subject them to heat from below (any heat put out by the fire will rise directly in front of the screen) and behind (does your chimney breast get quite warm to the touch ?), then it may struggle to keep cool.
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That's not actually correct (well, certainly not in my case).
Put the fire on and hold your hand against the wall above it, where you'd want the TV to be placed. See if it feels hot. Slowly pull your hand away from the wall. In my case, when I did this the area close to the wall was no warmer than the rest of the room (guess the heat radiates rather than just rising up) but pull your hand away and 8 inches or so from the wall it would start getting warmer. I guess how close to the wall the heat gets will depend on whether you have a mantle piece, how deep it is, the fire's output etc. Do you actually use the fire anyway? We never really used ours so I took it out in the end.
Our Panasonic Plasma was over the fireplace for about 7 years and never had any issues (although it was actually too high really - now it's lower it's much better).