  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.
