The problem with using a chair is that the amount of help your legs offer varies. The natural inclination is to get more lift from your legs as you arms get more tired.
If you use a pull up assist band , you can set the length, which fixes the amount of lift, and then struggle to get your numbers up. As you get stronger, you lengthen the band, the assist is less, and you get stronger still.
I bought this one for $30 from sports authority about a year ago
Dont know why the price went up to $50.