This chair is called the Stokke Gravity™ balans®. From the website:
From a comfortable working position to a reclined position and a feeling of almost weightless. The sloping seat allows wider space between the thigh and the upper part of the body, while the leg cushions prevent sliding forward when working at a table. When leaning back your legs will be lifted higher than your head providing you with the best position for relaxation and well-being!
After seeing the “functionality†demonstration, I want to try this out! Link
Everyone agreed that the original "balans" chairs were comfortable, but after trying them, they went back to regular chairs.