Heat grill to medium-high heat. Season chicken with a little olive oil, salt, and pepper. Grill chicken, turning regularly. The internal temperature should be at least 165 degrees F (chicken should be white throughout).
Brush endives with olive oil. Grill until lightly charred and just tender. Turn regularly. Remove endive and tent with foil to steam for about 10 minutes. Season with light drizzle of olive oil, salt, and pepper.