1 tablespoon extra-virgin olive oil, plus more for brushing
2 Thai chiles, minced
1/2 cup crème fraîche
1 tablespoon red miso paste
1 tablespoon fresh lime juice
Four 6-ounce skinless, boneless chicken breast halves, pounded 1/4 inch thick
Salt and freshly ground pepper
4 cups lightly packed frisée lettuce, torn into bite-size pieces
Using a sharp knife, peel the grapefruits, removing all of the bitter white pith. Working over a bowl, cut in between the membranes to release the grapefruit sections. Add 1 tablespoon of the olive oil and 1 of the chiles.
Light a grill or preheat the broiler. In a small bowl, whisk the crème fraîche with the remaining chile, the miso paste and lime juice.
Brush the chicken breasts with olive oil and season with salt and pepper. Grill over a hot fire or broil until lightly charred and just cooked, about 3 minutes per side.
Mound the frisée on plates. Set a chicken breast on top. Drizzle the crème fraîche–miso sauce over the chicken and around the plates, scatter the grapefruit sections next to the chicken and serve.