We give a \#NC$^1$ upper bound for the problem of counting accepting paths in any fixed visibly pushdown automaton. Our algorithm involves a non-trivial adaptation of the arithmetic formula evaluation algorithm of Buss, Cook, Gupta, Ramachandran (BCGR: SICOMP 21(4), 1992). We also show that the problem is \#NC$^1$ hard. Our results show that the difference between \#BWBP and \#NC$^1$ is captured exactly by the addition of a visible stack to a nondeterministic finite-state automata.