Probably not an obelisk lol...
As ever with these, the answer seems to be "actually a bit more complicated than that".  Wikipedia describes it as a "navigation beacon": https://en.wikipedia.org/wiki/Chaldon_Hill , elsewhere https://trigpointing.uk/trig/8861 it's an "Admiralty Navigation Beacon".  It's certainly a beacon in the "you can see it from afar" sense, but whether it ever had a basket of burning wood attached I've no idea.
There are lots of OSMers in that general area and/or with a historic interest in these sorts of things - perhaps ask in the UK forum?
