Place a baking sheet on the top oven rack and preheat to 475 degrees F. Season the chicken thighs with salt and pepper; arrange skin-side up on the hot baking sheet, leaving some space between each piece. Bake until the chicken is cooked through and the skin is crisp, 25 to 30 minutes.
Meanwhile, heat the olive oil in a large skillet over medium heat. Add the squash, leeks and 1/2 cup water. Cover and cook until the squash is almost tender and the leeks are softened, 6 to 7 minutes. Add the sage, escarole and 1/4 cup water; season with 1/2 teaspoon salt and a few grinds of pepper. Cover and cook until the escarole is wilted, 6 to 7 minutes.
Gently stir the mustard and maple syrup into the skillet. Season with salt and pepper. Serve the chicken with the squash and escarole.