Preheat grill to medium-high heat.
In a small bowl, whisk together the lemon juice, olive oil, minced garlic, dried thyme, dried rosemary, dried oregano, salt, and pepper.
Place the chicken breasts in a shallow dish and pour the marinade over them. Let marinate for 10 minutes.
While the chicken is marinating, prepare the rice pilaf. In a medium saucepan, heat 1 tablespoon of olive oil over medium heat. Add the diced onion, carrot, and celery, and cook until the vegetables are tender, about 5 minutes.
Add the basmati rice to the saucepan and stir to coat in the oil. Cook for 1-2 minutes, until the rice is slightly toasted.
Pour in the chicken broth and bring to a boil. Reduce heat to low, cover, and simmer for 15 minutes, or until the rice is tender and the liquid is absorbed.
While the rice is cooking, grill the chicken breasts for 6-7 minutes per side, or until cooked through and no longer pink in the center.
Remove the chicken from the grill and let rest for a few minutes before slicing.
Fluff the cooked rice pilaf with a fork, then stir in the frozen peas and chopped parsley. Cover and let sit for 5 minutes, or until the peas are heated through.
Serve the grilled chicken with a generous scoop of rice pilaf.