Cover each chicken breast with plastic wrap and lightly flatten with a rolling pin or meat mallet. Season both sides with ground pepper.
Heat a 12-inch skillet over medium heat, add the butter and melt. Add the chicken and cook for 3-4 minutes per side, until browned and mostly cooked through. Remove to a plate and keep warm.
Reduce heat to low and add the onion. Cook for 2-3 mins, stirring, until soft. Increase heat to medium, add wine, and simmer for 1 minute. Stir in the cream and cook for another 3 minutes, until slightly reduced. Stir in the basil and season with salt and pepper, if desired.
Return chicken to the skillet and cook for a minute, until heated through. Serve with sauce and your favorite sides!