Preheat oven to 350. Place chicken breasts on a sheet pan, drizzle on olive oil and season with salt and pepper. When the oven is ready, place the chicken in the oven and roast for about 30-40 minutes. Let cool to handle. Shred or dice chicken.
Place chicken, onion, apricots, and almonds in a large mixing bowl. In a separate bowl, mix the yogurt, mayo, dill, vinegar, sugar, mustard, salt and pepper. You will probably need about 1 tbsp of salt and 1 tbsp of pepper.
Pour the dressing on top of the chicken and combine. Taste for seasoning. Serve immediately or refrigerate.