Turn the chair over so that the underside is visible.
Look for a piece that appears bent or warped. This is the broken piece that must be replaced. As a general rule, the entire section of the mechanism, not just that single piece, should be replaced just in case the damage was tension related.
Unscrew the old piece and take it to a furniture repair shop. Most models will have between two and four screws holding each piece in place. Alternatively, search for the particular model online at a parts supply website. Make sure to buy the exact piece.
Install the new piece by screwing it tightly into position.