Of course one-handed keyboards exist. Sure, it's not a peripheral you'd give much thought to (if ever), but circumstances could necessitate the need for a typing device you can use with a single limb. Maltron is one such provider and its range of Single Hand keyboards look as futuristic as they do retro.
Image: Ergo Canada
While it looks unusable at first glance, it's clear plenty of thought went into the ergonomics. In fact, Maltron itself claims that typing rates of 85 words per minute are possible and the design itself has prompted no strain or RSI complaints in over a decade.
And yes, it comes in left and right-handed models. I guess you could have one for both hands simultaneously, but at that point, perhaps a regular keyboard is in order.
If you want to see the Maltron in action, here's a rather boring video of exactly that. Fair warning, the audio isn't great.