Heat oil in a large skillet over high. Sprinkle chicken with pepper and 1/2 teaspoon salt. Add chicken to skillet; cook until browned on one side, 5 to 6 minutes. Remove from skillet.
Add grapes to skillet; cook, stirring occasionally, until skins are slightly charred, about 3 minutes. Add shallots and cardamom; cook, stirring often, until shallots are translucent and grapes begin to burst, about 3 minutes. Add chicken, browned side up, stock, and vinegar. Bring to a boil; reduce heat to medium, and simmer until grapes release their liquid, 3 to 4 minutes.
Remove chicken from skillet. Add parsley, butter, and remaining 1/4 teaspoon salt to skillet; stir to combine. Return chicken to skillet. Spoon sauce over chicken to serve.