  On the lattice $\widetilde{\mathbb Z}^2_+:={(x,y)\in \mathbb Z \times \mathbb
Z_+\colon x+y \text{is even}}$ we consider the following oriented
(northwest-northeast) site percolation: the lines $H_i:={(x,y)\in \widetilde
{\mathbb Z}^2_+ \colon y=i}$ are first declared to be bad or good with
probabilities $\de$ and $1-\de$ respectively, independently of each other.
Given the configuration of lines, sites on good lines are open with probability
$p_{_G}>p_c$, the critical probability for the standard oriented site
percolation on $\mathbb Z_+ \times \mathbb Z_+$, and sites on bad lines are
open with probability $p_{_B}$, some small positive number, independently of
each other. We show that given any pair $p_{_G}>p_c$ and $p_{_B}>0$, there
exists a $\delta (p_{_G}, p_{_B})>0$ small enough, so that for $\delta \le
\delta(p_G,p_B)$ there is a strictly positive probability of oriented
percolation to infinity from the origin.
