Ouldridge is a box-to-box midfielder who signed his first professional contract in the summer.
Chippenham boss Mark Collier said: “Tommy has trained a couple of times with us, he will add to the squad and is aware of the current competition for places in midfield.”
Ouldridge joins Swindon team-mate Scott Twine at Hardenhuish Park and will go straight into the Bluebirds squad for their clash against Welling United today.