Preheat the oven to 400 degrees F and grease a large baking dish with the oil.
Coat the chicken in lemon zest, salt, and pepper, then wrap each filet with two slices of prosciutto and place into the baking dish.
Bake the chicken for 15 minutes. Meanwhile, combine the jam and lemon juice.
When the 15 minutes are up, add the kale to the baking dish and pour the strawberry sauce on top. Return to the oven for another 10-15 minutes or until the kale is wilted and the chicken is cooked through.