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Heat oil in a large non-stick frying pan over medium-high heat. Add the onion and garlic. Cook, stirring often, for 5 minutes or until softened. Add the thyme and chicken. Cook, stirring, for 3 minutes or until chicken is light golden.
Add the cream and 180ml (¾ cup) water to the pan. Bring to the boil. Add the tortellini. Simmer, stirring occasionally, for 6 minutes or until mixture is thickened and tortellini is tender. Season. Stir in the shallot, 40g (½ cup) of the cheese and half of the parsley and chives until combined.
Serve pasta topped with the remaining cheese, sprinkled with the remaining herbs.