In a large mixing bowl or glass measuring cup, combine all the ingredients for the marinade and whisk until well combined.
Place the chicken breasts in a baking dish that's just big enough to accomodate them in a single layer and then pour the marinade right over. Toss delicately until all the chicken breasts are evenly coated, cover with plastic film and place in the refrigerator to marinate for at least 4 hours, or up to overnight.
Preheat your oven to 375°F.
In a large, heavy skillet, heat a few tablespoons of healthy cooking oil or fat over medium-high heat. Once the pan is hot enough, add the chicken breasts, 2 or 3 at a time, and sear for a minute or two on each side, until nice and golden brown.
Place the seared chicken breasts in a Dutch oven or other oven safe dish with tight fitting lid and repeat with the remaining chicken breasts.
Pour the remaining marinade over the chicken breasts, put the lid on and and bake in the oven for 25 minutes, then remove the lid and continue cooking for another 5 minutes to crisp up the chicken.
Serve immediately, drizzled with the cooking juices and garnished with slices of lime and a handful of freshly chopped parsley.