This paper addresses the issue of autonomous competitive yet safe driving in the context of the Indy Autonomous Challenge (IAC) simulation race. The IAC is the first multi-vehicle autonomous head-to-head competition, reaching speeds of 300 km/h along an oval track modeled after the Indianapolis Motor Speedway (IMS). We present a racing controller that attempts to maximize progress along the track while avoiding collisions with opponent vehicles and obeying the race rules. To this end, the racing controller first computes a race line offline. During the race, it repeatedly computes a small set of dynamically feasible maneuver candidates, each tested for collision with the opponent vehicles. It then selects a collision-free maneuver that maximizes the progress along the track and obeys the race rules. Our controller was tested in a 6-vehicle simulation, managing to run competitively with no collision over 30 laps. In addition, it managed to drive within a close range of the leading vehicle during most of the IAC final simulation race.