Place chicken in a zip-top bag, add oil, lemon zest and juice, salt and pepper. Seal and refrigerate until ready to cook, but no longer than 2 hours.
Cut feta block in half lengthwise and then each into six slices widthwise.
Fresh Herb Butter: In a small bowl, combine butter, lemon zest and juice, basil, parsley, chives, salt and pepper; mix well.
Remove chicken breasts from bag and discard marinade. Cut 3 slits about 1-inch (2.5 cm) apart widthwise on the top of each chicken breast being careful not to cut right through.
Place a tsp (5 mL) of herb butter and 1 slice of feta cheese into each slit.
Set air fryer to 350°F (180°C) and cook for 20 minutes or until chicken reaches an internal temperature of 165°F (74°C). If you have a chicken setting on your air fryer, use that.