Flatten each chicken breast to 1/4-inch thickness with a meat mallet; season with salt and pepper.
Mix spinach, feta, Greek yogurt, garlic, and oregano in a bowl until combined.
Spoon filling onto each breast, roll tightly, and secure with toothpicks or twine.
Heat olive oil in an ovenproof skillet over medium-high and brown roll-ups on all sides, about 6 minutes.
Transfer skillet to a 375°F oven and bake 15–20 minutes, until internal temp reaches 165°F.
Let rest 5 minutes, remove toothpicks, slice, and serve.