  We present a new chiral expansion scheme for the nucleon-nucleon scattering
amplitude which preserves unitarity exactly. Our effective field theory builds
on the power counting rules for 2-nucleon reducible diagrams proposed in
\cite{lutz}. We evaluate the leading order terms of the isospin one scattering
amplitude and elaborate in detail on the $^1S_0$ phase shift. Our chiral
description of the $^1S_0$-phase shift does compete in quality with modern
phenomenological nucleon-nucleon potentials. We describe elastic and inelastic
scattering quantitatively up to laboratory energies of $E_{\rm lab} \simeq 600$
MeV.
