Toast orzo in Dutch oven over medium-high heat until deep brown, about 5 minutes. Transfer to bowl. Heat 1 tablespoon oil in now-empty pot until shimmering. Cook asparagus until lightly browned and nearly tender, about 3 minutes. Transfer to plate.
Season chicken with salt and pepper. Heat remaining oil in now-empty pot until just smoking. Cook chicken until lightly browned, about 3 minutes per side. Transfer chicken to plate, leaving fat in pan. Add rice, onion, and 3/4 teaspoon salt to pot and cook until rice is sizzling and toasted, about 3 minutes. Add three-quarters garlic and cook until fragrant, about 30 seconds. Stir in toasted orzo, broth, and wine and bring to simmer. Nestle chicken into rice and pour in any juices accumulated on plate. Cover pot, reduce heat to low, and simmer until chicken is cooked through, about 12 minutes.
Working quickly, transfer chicken to plate and cover loosely with foil. Stir rice, replace cover, and continue cooking until rice is tender and liquid is absorbed, about 12 minutes. Off heat, gently fold in peas, basil, zest, remaining garlic, and reserved asparagus. Cover and let sit until heated through, about 2 minutes. Transfer to serving platter and top with chicken. Serve.
*note The rice will cook unevenly if the pot is uncovered for too long, so work quickly in step 3.