Pat your chicken breasts dry with paper towels and season both sides lightly with salt, pepper, and half of the Old Bay seasoning.
Heat olive oil in a large skillet over medium-high heat. Once hot, add the chicken breasts and sear for about 4-5 minutes on each side until golden brown and cooked through. Remove from the skillet and set aside.
In a mixing bowl, combine the softened cream cheese, sour cream, remaining Old Bay seasoning, lemon juice, and shredded cheddar cheese. Mix until smooth and creamy.
Gently fold the crab meat and half of the chopped parsley into the sauce mixture.
Return the chicken breasts to the skillet over low heat. Spoon the creamy crab sauce generously over each breast. Cover the skillet and let everything warm together for 3-4 minutes, allowing the cheese to melt and flavors to meld.
Sprinkle the remaining parsley over the top, and if you like, add an extra squeeze of fresh lemon juice. Serve immediately with your favorite side dish.