Sprinkle thyme, salt, and pepper over 1 side of chicken.
Heat oil in a large nonstick skillet over medium-high heat. Add chicken, seasoned side down; cook 4 minutes or until browned. Turn chicken; cook 3 minutes.
Transfer chicken to a plate; set aside and keep warm. Add rice to pan; cook, stirring constantly, 1 minute. Add tomatoes and broth; bring to a simmer. Return chicken to pan; cover, and simmer over medium-low heat 20 minutes or until chicken is done and rice is tender. Sprinkle chicken with parsley.