In this contribution the optimal boundary control problem for a first order nonlinear, nonlocal hyperbolic PDE is studied. Motivated by various applications ranging from re-entrant manufacturing systems to particle synthesis processes, we establish the regularity of solutions for W-1,W-p-data. Based on a general L-2 tracking type cost functional, the existence, uniqueness, and regularity of the adjoint system in W-1,W-p is derived using the special structure induced from the nonlocal flux function of the state equation. The assumption of W-1,W-p-and not L-p-regularity comes thereby due to the fact that the adjoint equation asks for more regularity to be well defined. This problem is discussed in detail, and we give a solution by defining a special type of cost functional, such that the corresponding optimality system is well defined.