Place each chicken breast half between 2 sheets of heavy-duty plastic wrap; pound to 1/2-inch thickness using a meat mallet or rolling pin. Sprinkle chicken evenly with salt and pepper.
Heat oil in a large nonstick skillet over medium heat. Add chicken; cook 6 minutes on each side or until done. Remove chicken from pan; keep warm.
Add wine to pan; bring to a boil, scraping pan to loosen browned bits. Cook until mixture is reduced to 1 tablespoon (about 1 minute). Add broth and thyme sprigs; cook until mixture is reduced to 1/2 cup (about 5 minutes). Remove from heat; discard thyme sprigs.
Add cheese to pan; stir with a whisk until smooth. Serve sauce over chicken; sprinkle with thyme leaves.
Wine note: While a wine lover might ask which wine goes best with chicken, in this dish, it's the goat cheese sauce, more than the chicken breasts, that deserves most of your pairing attention. Goat cheese is an ideal partner for sauvignon blanc. Both goat cheese and the sauvignon blanc have clean, fresh, tangy, earthy flavors, so the food and wine mirror each other. A sauvignon blanc I love for the flavor: Tin Roof Sauvignon Blanc from the North Coast of California--about $9. -Karen MacNeil