Grilled lemon chicken with oregano

Ok, so I love lemons and their flavor, but I have a hard time with lemon chicken for some reason. It always seems a little dry and "puckery" to me. I've tried many recipes and this one turned out the moistest (is that a word?) so far. There was still something missing though, not sure what...but my kids LOVED it and I will definitely be making it again. They liked sqeezing the grilled lemons over the chicken before they ate it. (and I thought it looked kind of fancy... but I'm kind of a geek. (This was adapted from www.recipegirl.blogspot.com)

1 T. grated lemon zest
1/3 c. fresh lemon juice (about 2 lemons)
1/4 c. finely chopped fresh oregano
1/4 c. finely chopped fresh parsley
2 T. olive oil
salt and pepper to taste
8 bonelss skinless chicken breast cutlets (the ones that are already cut thin).
4 medium lemons, halved

Prepare marinade:
In a small bowl, whisk lemon zest and juice, oregano, oil, 2 t. coarse salt and 1 t. pepper. Place chicken and marinade in large ziplock bag and set aside for 30 minutes at room temp, turning bags occasionally.
Preheat grill, brush grates with some olive oil to prevent sticking. Remove chicken from marinade and pat dry with paper towels. Place chicken on grill and cook until done (about 10 minutes if you have the thin cutlets). Transfer chicken to cutting board, tent with foil and let rest. Meanwhile, place lemon halves on the grill, cut side down and cook until slightly charred. Serve chicken breasts with lemon halves.
We had green beans and fruit with this and it was really pretty good.