Combine 1 cup broth, rice, and 3⁄4 teaspoon salt in large bowl. Cover tightly with plastic wrap and microwave until broth is completely absorbed, about 8 minutes. Meanwhile, pat chicken dry with paper towels and season with salt and pepper. Melt 2 tablespoons butter in large skillet over medium-high heat. Cook chicken until golden brown, about 3 minutes per side. Transfer to plate.

Melt remaining butter in now-empty skillet. Cook zucchini and corn until browned, about 3 minutes. Transfer to medium bowl. Add parcooked rice and remaining broth to skillet and bring to boil. Return chicken, along with any accumulated juices, to skillet and cook, covered, over medium-low heat until chicken is cooked through and rice is tender, 12 to 15 minutes. Transfer chicken to cutting board and tent with foil. Stir vegetables and scallions into rice, cover, and let sit until heated through, about 2 minutes. Slice chicken and serve with rice.