How to Make It
In a bowl, combine 1/2 cup of the oil with the vinegar, garlic, lemon zest and crushed red pepper. Add the chicken breasts and turn to coat evenly. Refrigerate for 1 hour, turning the breasts.
In a mortar, crush the oregano, thyme and 1/2 teaspoon of salt. Stir in the lemon juice and 1/3 cup of the olive oil and season with salt and pepper.
In a large cast-iron skillet, heat the remaining 1/2 cup of oil until shimmering. Add the potatoes in an even layer and cook over moderate heat until browned on the bottom, about 15 minutes; lower the heat halfway through cooking. Stir the potatoes and cook until browned all over, about 10 minutes longer. Add the onion and cook over moderate heat, stirring, until beginning to brown. Season with salt and pepper.
Light a grill or heat a grill pan. Remove the chicken breasts from the marinade and season with salt and pepper. Grill the chicken over a moderately hot fire until charred and cooked through, about 5 minutes per side. Transfer to a platter.
Warm the potatoes over high heat, stirring, until sizzling. Add the tomatoes and cook, stirring, for 1 minute. Spoon the herb sauce over the chicken and serve at once with the potatoes.