Heat olive oil in a skillet over medium heat and cook chicken breast halves until browned on both sides, 5 to 8 minutes per side.
Pour in chicken stock, artichoke hearts, pearl onions, thyme, salt, and black pepper and bring to a boil. Reduce heat to low and simmer until stock is reduced and onions and artichokes are tender, about 45 minutes; turn chicken breasts over in the skillet after 20 minutes.
Place a goat cheese slice on each chicken breast; cover skillet and let goat cheese melt.
Place chicken breasts onto a serving platter. Spoon about 3 tablespoons liquid from skillet into a small bowl and whisk in cornstarch until smooth; stir cornstarch mixture into skillet and cook until sauce has thickened, about 1 minute.