This is the Circus of Domitian, a 500 foot long exercise yard that was part of Emperor Domitian's palace in 81 A.D. Rick Steves notes that a poet of the day described the palace as being grand enough to "make Jupiter jealous."

It was once a single oval racetrack, but it also held gardens and strolling paths. Here's what they think it used to look like (before they added the oval track you can see in my picture):