Heat the oven to 450 degrees F. In a small bowl or measuring cup, stir together ½ cup olive oil and lemon juice to combine. Season to taste with salt and pepper.
Transfer ¼ cup of the dressing to a medium bowl and stir in the mustard. Pat the chicken dry, season both sides with salt and pepper, then add to the mustard-lemon mixture and turn to coat. Let marinate for at least 15 minutes.
Meanwhile, trim the radishes of their leaves. Thinly slice two of the radishes and reserve for serving. Halve the remaining radishes if they’re small; quarter large ones.
Transfer the halved or quartered radishes to a baking sheet, toss with just enough olive oil to coat, and season with salt and pepper. Move the radishes to one side of the pan, cut-side down, and add the chicken to the other side. Roast for 10 minutes, then add the escarole or romaine, drizzle to coat with oil, and season with salt and pepper. (You may need to use a second baking sheet depending on the size of your ingredients. If your radishes are already golden brown, remove them before adding the greens.)
Roast until the chicken is cooked through and has reached an internal temperature of 165 degrees F and the radishes and lettuce are golden brown on one side, at least 5 to 7 minutes more.
Thinly slice the chicken, then place on a serving platter with the roasted radishes and escarole. Add the reserved sliced radishes and the olives and sprinkle with chives. Drizzle dressing over top and season with salt and pepper to taste. Serve immediately.