Season chicken. Pat the chicken breasts dry with paper towels, then season both sides generously with salt and pepper and rub them with the olive oil. Dry chicken browns better, so do not skip the patting.
Cut the onion. Peel the onion, cut it in half, and slice it into thin half-moons.
Fry the chicken. Heat a 12-inch (28 cm) skillet over medium-high heat for about 2 minutes. Add the chicken breasts and fry for 6 to 7 minutes without moving them, until golden brown underneath.
Flip the chicken and add onion. Flip the chicken to the other side. Immediately add the sliced onions to the empty space in the pan and stir them regularly so they soften without burning. Cook for another 5 to 6 minutes.
Add cream. When the chicken is almost cooked through, pour in the cream. Let it bubble gently for 2 to 3 minutes until it thickens slightly and coats the onions. Then taste and adjust the salt and pepper.
Finish and serve. Turn off the heat once the chicken is cooked through. Transfer the juicy breasts to individual plates and spoon the rich, creamy onion sauce generously over the top to capture all the caramelized flavor. Serve this quick skillet dinner alongside your favorite side dish, like fluffy white rice, to soak up every drop of the luxurious, no-cheese pan sauce.