How to Make It
Preheat the broiler. In a large bowl, combine 1/2 cup of the olive oil with the thyme, brown sugar, chiles and a generous pinch of pepper. Reserve one-third of the marinade in a small bowl. Add the chicken pieces to the remaining marinade and turn to coat. Transfer the chicken to a broiling pan; broil 8 inches from the heat for about 35 minutes, turning once, or until cooked through.
Set the feta on a small baking sheet and brush with the reserved marinade. Broil, turning once, for about 2 minutes, or until sizzling and golden.
In a large bowl, whisk the remaining 2 tablespoons of olive oil with the vinegar. Add the arugula, season with salt and pepper and toss well. Arrange the salad, chicken and feta on 4 plates and serve.