Combine the ingredients for the marinade in a bowl. Taste to check the seasoning.
Add the chicken fillets to a plastic bag and pour the marinade over the chicken. Close the bag, massage and turn the chicken fillets to make sure all parts are covered with the marinade. Place in the fridge for at least 30 minutes, but preferably over night.
Preheat the oven to 150 degrees Celsius.
Preheat a pan over medium/high heat with some olive oil.
When the pan is really hot add the chicken to the pan and fry for 2-3 minutes on each side, until the chicken starts to get browned/blackened.
Place in an oven safe baking pan and bake in the oven for 15-20 minutes, depending on how thick your chicken fillets are. The inner temperature should be 70-72 degrees C.
Meanwhile place arugula on two plates, top add the burrata and sliced cherry tomatoes.
When the chicken is ready take it out from the oven, let it rest for 2-3 minutes in the pan.
Slice the chicken, place on the plates, top with thick balsamic vinegar and black pepper.