Prep the oven and pan. Heat the oven to 400°F (205°C).
Line a baking sheet with foil and set a wire rack on top if you have one. This helps the bacon crisp and keeps the chicken from sitting in grease.
Make the cheese filling. In a bowl, combine cream cheese, shredded cheese, garlic, smoked paprika, onion powder, thyme, salt, and pepper. Mix until smooth and spreadable.
Butterfly the chicken. Place a hand flat on each chicken breast and slice horizontally to make a pocket, stopping about 1/2 inch from the other side.
Don’t cut all the way through. Season the inside lightly with salt and pepper.
Stuff it. Spoon the cheese mixture evenly into each pocket. Press the top flap down gently to seal.
If any filling sneaks out, just nudge it back in.
Wrap with bacon. Lay 2–3 slices of bacon per breast, slightly overlapping, and wrap them around the chicken from one end to the other. Tuck the ends under or secure with toothpicks. Aim for full coverage to keep the cheese inside.
Optional quick sear. For extra-crispy bacon, heat a large skillet over medium-high with a splash of olive oil.
Sear wrapped chicken 1–2 minutes per side to jump-start browning. Transfer to the prepared rack.
Bake. Place the chicken on the rack and bake for 22–28 minutes, depending on thickness. Start checking at 20 minutes.
The chicken is done when a thermometer reads 165°F (74°C) in the thickest part.
Finish under the broiler. If the bacon needs more color, broil on high for 1–3 minutes. Watch closely so it doesn’t burn.
Rest and serve. Let the chicken rest for 5 minutes to keep the juices in. Slice and serve with your favorite sides.