Each bicycle shall be equipped with a brake which enables the operator to cause the braked wheels to skid on dry, level, clean pavement; provided, that a fixed gear bicycle is not required to have a separate brake, but an operator of a fixed gear bicycle shall be able to stop the bicycle using the pedals.
18 DCMR 1204.1
The portion of D.C.'s law which precedes the semi-colon, reflects existing law in many jurisdictions in the U.S., including Chicago's ordinance dealing with bicycle brakes. As I've noted in the past, this language alone sufficiently accommodates fixed gear riders. Even the added clarification to the D.C. law acknowledges this. The code states that fixed gear riders need not have a "separate brake," evidencing the authors' recognition that fixed gear bikes already have one brake in the form of the fixed gear drive train itself. However, the added language is undoubtedly a helpful clarification for law enforcement officers and judges who may be unfamiliar with how bicyclists who operate a fixed rear hub may bring their bikes to a halt.
If any readers are aware of any other jurisdictions that explicitly permit fixed gear braking I would certainly appreciate a heads-up.