In a small bowl, combine feta and oregano. Make a pocket in chicken breasts: Holding chicken flat with palm of one hand, make an incision in thicker side of each breast with a paring knife. Carefully pivot the knife to create a deep pocket, keeping the other side of the chicken breast intact. Stuff pockets with feta mixture, dividing evenly; generously season both sides of chicken with salt and pepper.
Heat oil in a large skillet over medium-high heat. Add chicken, and cook until browned on both sides, 6 to 7 minutes per side.
Cover skillet, and continue cooking until chicken is opaque throughout and an instant-read thermometer inserted into thickest part registers 160 degrees. about 5 minutes more. Remove chicken to a platter, and keep warm.
To the skillet, add chicken stock, and cook, stirring up brown bits with a wooden spoon until reduced slightly. Add lemon juice and butter. Reduce the heat to low, and swirl pan until butter is melted, and sauce is slightly thickened. Serve chicken drizzled with sauce.