I am apparently very into the whole hybrid class thing right now, and Chaise Fitness absolutely falls into that category. When you first hear you are working with a "chair" images of a sexy little strip tease may come to mind. At least it did for a colleague of mine...but the word chair is used very liberally here. 
I took the Reinvention class, as this is their signature class and I wanted to start with the basics. I arrived 15 minutes before class, as instructed to get a tutorial in the chair. Cat (the instructor) showed me some basic moves and introduced me to the bungees and how not to fall off. The chair is more like a padded stool, with a bar that you push down on and you adjust the resistance to make it harder. Then you have these bungees that are suspended from the ceiling. They are there both to work your arms and hold you up. 
Here's something else I learned while being there early....people LOVE Cat. She had recently gotten engaged and her regulars were just so excited for her and brought her gifts. It was a really sweet thing to see.
Anyway, the class itself is a combination of pilates, barre, a little ballet and aerobics.
Cat had us performing pumping moves with our arms in the bungees, core work while balancing on the chair and leg work balancing on the chair while utilizing a small ball. We did some tricep dips off the side of the chair as well as boat poses and C curves while sitting on the chair.
One of the moves that I felt a little uncomfortable in was a signature chair move included lying on one side on the chair with legs straight and one arm resting on the bar while the top arm remained in the bungee and extended straight. We then pushed down on the bar lowering it towards the ground and back up again. This created tension in our arms and core and although we were lying on the chair, we still needed to maintain our balance.
Pikes were also pretty tough, in the fact that you really have to engage your core the ENTIRE time so that you don't hit the ground at all. We stand on the bar with our hands on the chair, using our abs we allowed the bar to lift off the ground and pushed it back down again in small pulsing movements that worked our abs and legs. A variation of this move included standing with one foot on the chair, knee bent and pushing the bar down with only one leg. 
They have several other classes, including a Cardio Chair, which was going on when I first got there. And truthfully it terrified me. I'm absolutely going to try it though.