In a medium bowl, season the chicken with salt and pepper. Add the flour and toss to coat.
In a large skillet, heat the olive oil over medium heat. Shaking off any excess flour, add the chicken to the skillet and cook, turning once, until browned, about 5 minutes total. Transfer to a platter.
Add the onion to the skillet and cook, stirring, over medium-high heat for 1 minute.
Add the chicken broth and blueberries; bring to a boil and cook until reduced by half, about 5 minutes.
Stir in the butter and season with salt and pepper.
Turn off the heat and return the chicken and any juices to the skillet.
Divide the chicken among 4 plates and spoon the sauce on top.