Slice the chicken breasts into 2 thin pieces. If they are already on the thin side, you could pound out the thicker side with a meat mallet.
Place the flour in a shallow bowl. Dredge the chicken pieces in the flour, coating both sides.
Melt 4 Tbsp of butter in a skillet over medium high heat. Once the butter is melted, add a single layer of the dredged chicken and let cook for 4 to 5 minutes. Flip and cook another 4 to 5 minutes on the other side, or until cooked through. If the butter and flour in the skillet begin to darken or even burn, reduce the heat to medium or medium low. Once the chicken is cooked, set aside on a plate.
Melt the other 4 Tbsp of butter to the same skillet and repeat cooking for the remaining dredged chicken pieces, both sides for 4 to 5 minutes. Monitor the heat level to keep the flour in the skillet from over-browning. Once cooked, add the chicken with the other cooked chicken.
To the same skillet, add the onion and garlic and saute for 1 minute, then pour in the chicken stock to deglaze the pan. Once the chicken stock is bubbling, add the Boursin cheese and whisk into a creamy sauce.
Once the creamy sauce begins to bubble, nestle the chicken pieces into the sauce and reduce heat to low until ready to serve.
Serve Skillet Boursin Chicken with your favorite veggie sides, plus rice or garlic bread. Enjoy!