I'll second this. Many years ago (late 80s... yes, I'm that old) I snapped a chain while skid-slowing my track bike on a steep downhill. Luckily, I was not in heavy traffic and was able to slow down on the coming uphill, but it was still pretty scary to not be able to stop at all. If there had been a busy intersection at the bottom of the hill, I would have had to bail at nearly 30 mph (or face a worse fate).

These days, I am older (and hopefully wiser), and I would never ride a fixed gear on the road without at least a front brake. Even riding to the velodrome, I use a front brake with a BMX lever that can be easily removed. Maybe using a brake is not considered cool by hipster standards, but better safe than sorry.