Combine cherries and Marsala in a small microwave-safe bowl. Microwave at high for 45 seconds, and set aside.
Heat oil in a large nonstick skillet over medium-high heat. Add chicken; cook 4 minutes on each side or until done. Remove chicken from pan; sprinkle with 1/4 teaspoon salt and 1/4 teaspoon pepper. Cover and keep warm.
Add butter to pan, and cook until butter melts. Add shallots and thyme; sauté 1 minute or until tender. Stir in broth, scraping pan to loosen browned bits. Add cherry mixture, remaining 1/4 teaspoon salt, and remaining 1/4 teaspoon pepper; bring to a boil. Reduce heat to medium, and simmer 2 minutes or until sauce is slightly thick. Serve chicken with sauce.