Place each chicken breast half between two pieces plastic wrap; pound lightly with the flat side of a meat mallet to a rectangle 1/4 to 1/2 inch thick.
In a small bowl combine 1 teaspoon of the olive oil, the thyme, 1 clove of the garlic, and the black pepper; mix well. Rub both sides of each chicken breast half with oil mixture. Set aside.
In a medium saucepan combine the water, broth, and wine; heat over high heat until hot but not boiling. Reduce heat to low; keep warm.
Meanwhile, in another medium saucepan heat the remaining 2 teaspoons olive oil over medium heat. Add corn and onion; cook 6 to 8 minutes or until corn is tender and onion is lightly browned. Add rice, mushrooms, and the remaining 2 cloves garlic; cook and stir about 5 minutes or until rice is golden brown, stirring frequently. Carefully add 1/2 cup of the broth mixture, stirring to loosen brown bits from bottom of saucepan. Bring to boiling; reduce heat. Simmer, uncovered, 3 to 4 minutes or until the rice has absorbed the liquid.
Add another 1/2 cup of the broth mixture. Cook and stir 3 to 4 minutes more or until the rice has absorbed the liquid. Continue adding broth mixture, 1/2 cup at a time, and cooking until all of the liquid has been absorbed before adding more, stirring often. (This should take 18 to 20 minutes total.)
Meanwhile, coat a large nonstick skillet with cooking spray; heat over medium heat. Add chicken. Cook about 6 minutes or until chicken is no longer pink (170°F), turning once halfway through cooking time.
When rice is fully cooked but still slightly firm, remove from heat. Stir in pea pods, tomato, Parmesan cheese, and the white pepper. Slice chicken crosswise.
Serve rice mixture topped with sliced chicken.
Make sure to look for a white wine or white wine vinegar that is listed as gluten free.