In this paper we give the distribution of the position of the particle in the
asymmetric simple exclusion process (ASEP) with the alternating initial condition. That is,
we find $\mathbb{P}(X_m(t) \leq x)$ where $X_m(t)$ is the position of the particle at time
$t$ which was at $m =2k-1, k \in \mathbb{Z}$ at $t=0.$ As in the ASEP with the step initial
condition, there arises a new combinatorial identity for the alternating initial condition,
and this identity relates the integrand to a determinantal form together with an extra
product.