Kosher salt and freshly ground black pepperto taste
Sprigs of fresh thymeoptional
Preheat the oven to 425°F with a rack placed in the center of the oven.
Place the onions with the wine, red wine vinegar and balsamic vinegar in a small saucepan and bring to a boil over high heat. Lower heat to a simmer, partially cover the pan and cook for about 10-15 minutes, until the onions are tender. Stir in the figs, garlic, honey, soy sauce, ginger and cayenne pepper, and cook for about 5 minutes more, or until the figs have softened but are not completely mushy. Remove from heat. Take approximately half of the mixture and blend it in a blender, and return it to the pan to thicken the sauce. Season to taste with salt. The fig chutney can be made several days in advance if you wish; cool and store in an airtight glass container in the refrigerator until ready for use.
Place the chicken breasts in a 9×13 baking pan and brush with melted butter. Season generously with salt and pepper, and fresh thyme (feel free to add your favorite seasonings, if you wish). Toss the potatoes with olive oil, season with salt and pepper, and arrange around the chicken. Roast in the oven for 18-20 minutes or until a thermometer inserted in the thickest part of the chicken registers 165°F.
Serve the chicken with the fig chutney sauce and fresh figs, if using.