Preheat the oven to 375 degrees F (190 degrees C).

Heat olive oil in a skillet over medium heat. Add spinach and garlic and cook, stirring, until the spinach has wilted, 3 to 4 minutes. Drain mixture in a sieve and squeeze out excess liquid; transfer to a mixing bowl. Mix in artichoke hearts, mayonnaise, Parmesan cheese, and feta cheese and stir until all ingredients are well combined.

Place chicken breasts in an ungreased 9x12-inch baking pan. Spread artichoke spinach mixture evenly over the chicken.

Bake in the preheated oven until the chicken juices run clear and the edges of the cheese topping are starting to brown, 25 to 30 minutes. Remove from the oven. Carefully pour out and discard excess liquid from the baking pan.

Set an oven rack about 6 inches from the heat source and preheat the oven's broiler.

Place the baking pan under the broiler and broil until the top of the cheese topping has browned a little more, 2 to 5 minutes.