In a large skillet, heat 2 tablespoons olive oil over medium-high heat. Season the chicken with salt and pepper and cook, turning once, until golden, 12 to 14 minutes. Transfer to a large plate and reserve the skillet.
Meanwhile, in a large pot of boiling salted water, cook the orzo until al dente, about 5 minutes. Drain and transfer to a large bowl. Toss with the remaining 2 tablespoons olive oil, half the basil and salt and pepper to taste. Cover to keep warm.
Set the skillet over medium-high heat; add the onion and mushrooms and cook, scraping up any browned bits from the pan, until softened, about 8 minutes. Stir in the tomatoes and their juice, the tomato sauce, capers and remaining basil; season with salt and pepper. Add the chicken to the sauce and bring to a boil. Lower the heat and simmer, stirring occasionally, until the chicken is cooked through and the sauce has thickened, 7 to 10 minutes. Transfer the chicken to 4 plates, top with the sauce and serve the orzo alongside.