$3{ imes}3{ imes}3$ is the meaningful smallest product of three chains of each size 2n+1 since $1{ imes}1{ imes}1$ is a 1-element poset. The linear discrepancy of the product of three chains $2n{ imes}2n{ imes}2n$ is found as $6n^3-2n^2-1$. But the case of the product of three chains $(2n + 1){ imes}(2n + 1){ imes}(2n + 1)$ is not known yet. In this paper, we determine ld$(3{ imes}3{ imes}3)$ as a case to determine the linear discrepancy of the product of three chains of each size 2n + 1.