In a small bowl combine the softened butter, parsley, chives, and lemon juice. Transfer the butter mixture to a small piece of plastic wrap, form it into a log, wrap it up tightly and refrigerate or freeze until very firm.
Place each chicken breast into a ziplock bag (or between 2 pieces of plastic wrap) and pound chicken until it is about 1/4" thick. Remove the chicken breasts from plastic and season with salt and pepper to taste.
Remove the butter mixture from the fridge/freezer and divide it into 4 equal portions. Place one portion in the center of each chicken breast. Fold the short edges of the breasts into the center, then roll the chicken until the butter is covered by the meat. Secure with wooden toothpicks.
Dip the chicken into the flour to coat, then dip the chicken into the egg, then dip the chicken into the breadcrumbs to coat well.
Chill the chicken breasts, either in the fridge for an hour or in the freezer for a half hour.
Preheat the oven to 425 F. Place a wire rack on top of a rimmed baking sheet. Place chicken onto the wire rack. Bake, uncovered, for 30 to 35 minutes, or until the internal temperature of the chicken reaches 165 F.