To prepare chicken, heat 2 teaspoons oil in a large nonstick skillet over medium-high heat. Sprinkle chicken with 1/4 teaspoon salt and pepper. Add chicken to pan; cook 4 minutes on each side or until browned. Remove chicken from pan.
Heat 1 teaspoon oil in pan over medium-high heat. Add onion, carrot, celery, and 2 garlic cloves. Cover and cook 5 minutes or until tender, stirring occasionally. Stir in wine, scraping pan to loosen browned bits. Stir in 1/2 teaspoon salt, tomato, basil, and rosemary; bring to a boil. Cover, reduce heat to medium-low, and cook 15 minutes.
Return chicken to pan. Cover and simmer 35 minutes or until chicken is done. Uncover and cook 5 minutes or until tomato mixture thickens.
To prepare polenta, combine milk and broth in a medium saucepan; bring to a boil. Remove from heat; gradually add instant polenta, stirring constantly with a whisk. Cover and cook over medium-low heat 2 minutes. Remove from heat; stir in cheese and 1/4 teaspoon salt.
To prepare gremolata, combine parsley, rind, and 1 garlic clove. Serve chicken mixture over polenta; sprinkle with gremolata.
Chicken thighs stand in well for veal shanks in osso buco; their higher fat content, compared to other chicken parts, lets them hold up to long cooking or braising.