The 26 year-old made a slow start to the bout, allowing the rangy Lee, 28, to take the centre of the ring and use his height and reach to arguably take the opening three rounds, although I did score the second even.
Chavez was able to gain a foothold from the fourth and back Lee onto the ropes on numerous occasions which brought sustained success over the next three rounds as he clearly possessed the heavier punches of the two.
The end came towards the end of the seventh when the Irishman was rocked by a one-two uppercut, followed by a sweet right hand and with Lee stumbling, referee Laurence Cole jumped in to stop the fight.
The stoppage may have been a little premature for my liking, but the Mexican world champion was taking over the fight and in the end, proved too much for Lee, who now drops his second loss in 30 bouts.
In chief support, IBF lightweight champion Miguel Vazquez won a ten-round non-title fight against Daniel Attah, taking the fight 100-90 on all three of the judges scorecards at the Sun Bowl in El Paso, Texas to move to 31-3.