Preheat the oven to 450 degrees . In a large bowl, whisk together 3 tablespoons olive oil, the lemon juice and balsamic vinegar; season with salt and pepper. Stir in the cannellini beans.
Place the tomatoes cut side up on a parchment-lined baking sheet. Drizzle the tomatoes with 1 tablespoon olive oil, season with salt and pepper and bake until very soft, about 30 minutes.
Meanwhile, preheat a grill pan over medium-high heat. Brush the chicken and scallions with the remaining 1 tablespoon olive oil, season with salt and grill, turning once, until the chicken is cooked through, about 8 minutes.
Add the lettuce to the bean mixture and toss to coat. Divide the salad among 4 plates and top with the tomatoes and scallions. Thinly slice the chicken on the diagonal and divide among the plates.