  We consider a system of $N$ bosons confined to a thin waveguide, i.e.\ to a
region of space within an $\varepsilon$-tube around a curve in $\mathbb{R}^3$.
We show that when taking simultaneously the NLS limit $N\to \infty$ and the
limit of strong confinement $\varepsilon\to 0$, the time-evolution of such a
system starting in a state close to a Bose-Einstein condensate is approximately
captured by a non-linear Schr\"odinger equation in one dimension. The strength
of the non-linearity in this Gross-Pitaevskii type equation depends on the
shape of the cross-section of the waveguide, while the "bending" and the
"twisting" of the waveguide contribute potential terms. Our analysis is based
on an approach to mean-field limits developed by Pickl.
