Whisk together oregano, vinegar, and 1 tablespoon oil. Brush marinade onto both sides of chicken. Transfer chicken to a nonreactive dish; cover, and refrigerate at least 2 hours or overnight.
Put remaining 2 tablespoons oil and the garlic into a large skillet. Cook over medium heat, stirring occasionally, until garlic has softened, about 2 minutes. Add beans and reserved liquid, and rosemary. Cook, mashing beans with the back of a wooden spoon, 5 minutes. Add 1/4 teaspoon salt; season with pepper. Transfer to a small bowl. Cover, and set aside
Heat a large grill pan over medium-high heat. Coat with cooking spray. Add chicken. Grill, turning once, until cooked through, 3 to 4 minutes per side. Season with remaining 1/2 teaspoon salt. Transfer to a plate; let cool slightly. Cut chicken into 1/4-inch-thick slices; set aside.
Toast bread. Spread each slice with white-bean spread, dividing evenly. Top 4 slices with the chicken, radishes, and escarole, and then the remaining bread.