Heat the oil and butter in a tagine or heavy-based casserole dish. Stir in the onion, chopped rosemary, ginger, and chiles and sauté until the onion begins to soften.
Add the chicken thighs and brown them on both sides. Toss in the apricots with the honey, then stir in the plum tomatoes to ensure there is enough liquid to cover the base of the tagine and submerge the apricots.
Bring the liquid to a boil, then reduce the heat. Cover with a lid and cook gently for 35-40 minutes.
Season to taste with salt and pepper. Shred the larger basil leaves and leave the small ones intact. Sprinkle them over the chicken and serve the dish immediately.