Heat the oil in a heavy-based pan and brown the chicken for 3-4 minutes on both sides. Remove and set aside.
Deglaze the pan with the chicken broth, stirring to release any juices from the chicken on the base of the pan.
Next, add the butter, garlic, cream, and 1 tablespoon of capers. Bring to a boil, reduce the heat to a gentle simmer.
Add the lemon juice and lemon zest. Stir to combine.
Return the par-cooked chicken breasts and any juices.
Continue to simmer, stirring occasionally, until the chicken has completely cooked and the sauce has thickened. This may take between 10-15 minutes, depending on the thickness of the chicken breasts. Be sure to turn the chicken halfway to ensure it's evenly cooked.
Add the remaining capers and chopped parsley.
Adjust seasoning to taste.
Serve the chicken breast with a drizzle of sauce and your favourite vegetables.
