I once saw a website where you could play this (under the name 'Turnless Chess'). The idea is that pieces take time to reach their destination (so that if you see this Queen coming at your King from large distance you have still time to side-step out of her path), and that after arriving on their target square, there is a 'dead time' that has to elapse before you can move that piece again. (You can move other pieces, though.)
Real-Time Chess
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Has anybody tried playing real-time chess, where chess is a real-time strategy game as opposed to turn-based?
I cannot imagine that it would end well :P