Yes I had a look, I couldn't find the cardinal chuck but the key I use on jacobs 34 chucks came with the
cardinal chuck. The key has a 5/16 pin and 11 teeth. The key I have is a jacobs and just has
a 3 on it, but it goes with 34 chucks so it shouldn't be a problem finding one.

The next size down key I have, which is for jacobs 32 chucks, has a 1/4 pin and 9 teeth.
The next size has a .375pin and 12 teeth, that is for the jacobs 36 chuck.