Whisk together the yogurt, 2 teaspoons of the oil, garlic, lemon juice and 1/2 teaspoon each salt and pepper in a medium bowl until well combined.
Bring a pot of water to a boil and preheat an outdoor or indoor grill to medium heat. Rub the chicken thighs with the remaining 1 teaspoon oil and sprinkle with 1/2 teaspoon pepper and 1/4 teaspoon salt. Grill until nicely marked and cooked through, 10 to 12 minutes per side. Transfer to a cutting board at let stand for at least 5 minutes.
Add the orzo to the boiling water and cook according to package directions for al dente, stirring in the peas the last minute of cooking. Drain the orzo and peas, reserving 1 cup of the cooking liquid. Stir the orzo and peas into the yogurt mixture, along with the goat cheese, 3 tablespoons of the fresh herbs and at least 3/4 cup of the cooking liquid, until well combined. Transfer to a platter.
Thinly slice the chicken and arrange on top of the orzo. Sprinkle with the lemon zest and the remaining 1 tablespoon fresh herbs and serve.