I don't know much about them, but I know a little to get you started in finding more information.
There are quite a few Chorded keyboards.
The ones most used are those used for live transcription in court rooms.
Chords are two-handed and each one will translate into a syllable -- not a letter.
They are reportedly very very fast when used by trained professionals.
VeloType is one such system.
On most other types of chord keyboards, a chord on a one-handed keyboard will translate into a single letter.
Each one would have its own system.. often patented so it can't be used by another manufacturer.
Some I have heard of are:
* microwriter - One of the oldest. More of a computer in its own right. Could record long texts input with one hand and then output them to a printer.
* Twiddler - Held in the hand.
* Data Egg - More of a two-way pager. Held in the hand like the Twiddler but a different input system.
* CyKey - has gone through a few revisions. Each chord was designed to resemble a glyph to be easy to learn.
* The Claw
* Accukey
*
BAT Keyboard. The only one I have ever tried (DT keyboard party 2013)
Then there are one-handed keyboards that are mostly like regular keyboards but where you would need to hold a modifier for another layer. Some people have them in the Chord keyboard category.
If I am not mistaken, the FrogPad is a such device.
You can see more of some of these in
The Buxton Collection - Chord Keyboard category. The Buxton Collection is an interesting collection of user-interface tech devices in general.