Place chicken in a resealable plastic bag. Combine marinade and 2 tablespoons olive oil; pour over chicken, seal and refrigerate overnight.
Preheat oven to 4235°F Place chicken on a parchment paper-lined baking tray; season with salt and pepper. Bake until chicken is fully cooked, about 25 minutes.
Meanwhile, prepare basmati rice according to package directons using the chicken broth. Microwave the peas with 1 tablespoons water in a covered dish for 2 minutes. Quickly run under cold water until cool, then drain well. Combine peas, chickpeas, cucumber, onion, mint, remaining olive oil and lemon juice. Season to taste.
Divide rice between 4 salad plates, top each with a sliced chicken breast, and chickpea salad.