PS: Had to post this with little deliberation, ASoS is my favorite book despite the Red Wedding (horrible event but GRRM's best written chapter...) and it's hard for me to narrow it down because I did enjoy them all, except for Dany.
My absolute favorite chapter in the book(and series) is the duel between Oberyn and the Mountain. It was so suspenseful and I was on the edge of my seat while reading. Trial by combats are always exciting and the stakes in this one are very high. You don't want anything bad to happen to Tyrion, and after the recent events of the Red Wedding, all bets were off. Oberyn was an incredible character established in very little time, the back story of his family is compelling and I felt overwhelming sympathy for Elia and the fate of her children. The Mountain is the biggest piece of shit in the series, and you so desperately want to see Oberyn kill the Mountain and get closure for his family. For a fleeting moment, it looks like that just might happen, and then... This is what I looked like after finishing that chapter: