Peal the skins from the shallots. Trim any fat from the chicken breasts and cut the breasts into 1" cubes (about the same size as the shallots). Coat the chicken pieces with salt and pepper on all sides. Melt 4 tablespoons of butter in a cast iron skillet on medium heat until just golden brown. Add the rosemary and sage. Add the shallots and cook until the butter is brown and the shallots are slightly soft, about 4 minutes. Transfer the shallots to the slowcooker and leave the butter in the skillet.
Add the chicken to the skillet. Cook the chicken in the butter until the chicken pieces are white on all sides, about 5 minutes. Pour the wine and balsamic into the skillet and turn the heat to high. Cook for 4 minutes. Transfer the chicken and butter to the slowcooker. Cover and cook on high for 3 hours or low for 6 hours.