The one-arm chin-up is a feat very few achieve. It’s perhaps the ultimate test of upper body pulling strength. There are no tricks to the one-arm chin-up; it’s a product of hard work and practice. If you want it, you have to work for it. Here are the steps:
Assume a dead hang position from one arm from a bar or a set of rings. Keep the shoulders sucked down.

As you can see, your body will naturally rotate sideways after you release one arm from the bar/ring.
Tighten everything up like you would with a normal chin-up and drive your elbow down hard.

Pull yourself up until your throat reaches the bar or rings.
Control back down to a full dead hang and repeat.
Ease yourself into the one-arm chin-up practice. Elbow tendonitis is common with this movement from overuse.
One way to start developing the strength for the one-arm chin-up is to practice holding positions throughout the movement for time. For example, practice holding just the top position for a few seconds, then the middle, and everywhere in between.