In a large skillet, heat olive oil over medium heat. Add chicken breasts; cook until lightly browned, 3 to 4 minutes per side. Remove chicken from pan; set aside, reserving drippings in skillet.
Add shallot and garlic to skillet; cook for 2 minutes, stirring constantly. Add mustard and fig preserves, stirring until preserves melt. Add cream, salt, and pepper, stirring to combine.
Return chicken to pan, and reduce heat to medium-low. Simmer, uncovered, until chicken is tender and sauce thickens slightly, 20 to 30 minutes. Turn chicken periodically for even cooking.