Brush chicken breasts on both sides with olive oil and sprinkle with salt and pepper, bake on a baking sheet for 35 to 40 minutes, until no longer pink in the center.
While chicken is baking, heat 1 tablespoon of olive oil in a large skillet over medium heat
Add onion, saute until translucent, about 5 minutes, stirring often so it does not burn.
Reduce heat to medium/low. Add blueberries, vinegar, thyme and a dash of salt and pepper to pan and stir well to blend. Cook for 25-30 minutes, stirring occassionally. Blueberries will break down and create a thick sauce. Remove from heat and set aside.
Remove chicken from oven and let cool slightly. When chicken has cooled enough to handle, shred and mix with caramelized onions and blueberries.
Divide arugula evenly between four bowls or plates. Top with chicken mixture and diced cucumbers. Drizzle a small amount of olive oil on top of each salad and finish with a spinkle of pepper. Can be served warm or cold.