To prepare chutney, combine first 11 ingredients in a medium saucepan; bring to a boil. Reduce heat to medium-low, and simmer 25 minutes or until thickened, stirring occasionally.
To prepare chicken, combine oil, basil, oregano, chicken, and 3 minced garlic cloves in a large heavy-duty zip-top bag; seal. Marinate in refrigerator for 2 hours, turning occasionally. Remove chicken from bag. Sprinkle 3/4 teaspoon salt and black pepper evenly over chicken.
Heat a large grill pan over medium-high heat. Cook the chicken 5 minutes on each side or until done. Serve with chutney.