Season the chicken breasts with a little bit of salt and pepper.
Melt some cooking fat in a heavy skillet (cast iron preferred) set over medium high heat. When the fat is nice and hot, add the chicken breasts and cook until a nice golden crust forms on each side and the meat is cooked through, about 5-7 minutes per side.
Remove chicken to a plate and add chanterelles to the skillet. Cook until slightly softened, about 2-3 minutes. Add to the plate with the reserved chicken.
Add onion, garlic, salt, pepper and rosemary to the skillet (and more fat if necessary) and cook until fragrant and the onion is translucent, about 4-5 minutes. Add white wine vinegar and chicken stock and bring to a simmer. Meanwhile, mix the tapioca starch and water together to form a slurry. Add that to the simmering stock and whisk until slightly thickened, about 30 seconds. Add goat cheese and stir until completely melted.
Tear or cut the chicken into bite size pieces and return to the skillet, along with the chanterelles, dried apricots and chopped pistachio. Stir to combine and serve.