The universal covering group \(\widetilde{\hbox{Homeo}}_ +(S^ 1)\) of \(\hbox{Homeo}_ +(S^ 1)\) is the subgroup of \(\hbox{Homeo}_ +(\mathbb{R})\) consisting of all \(\tilde f\) that commute with translation by 1. A theorem of Eisenbud, Hirsch, and Neumann asserts that \(\tilde f\in \widetilde{\hbox{Homeo}}_ +(S^ 1)\) is a product of \(k\) commutators if and only if \(\overline m(\tilde f)1- 2k\), \(\overline m(\tilde f)\) and \(\underline{m}(\tilde f)\) being the maximum and minimum values, respectively, of \(f(x)-x\) on \(\mathbb{R}\). The author shows that the \(PL\) version of this theorem fails. He also proves that translation \(T_ a: \mathbb{R}\to\mathbb{R}\) by \(a\in\mathbb{R}\) is a product of \(k\geq 1\) commutators in \(\widetilde {PL}_ +(S^ 1)\) if and only if \(| a|<2k-1\). This is applied to obtain the piecewise linear version of a theorem of Milnor and Wood: An oriented, \(C^ 0\) circle bundle \(E\) over a closed, oriented surface \(\Sigma\) of genus \(\geq 1\) admits a transversely \(PL\) foliation transverse to the fibers if and only if \(| \text{eu}(E)|\leq |\chi(\Sigma)|\).