  We consider the dynamics of $N$ interacting bosons initially forming a
Bose-Einstein condensate. Due to an external trapping potential, the bosons are
strongly confined in two dimensions, where the transverse extension of the trap
is of order $\varepsilon$. The non-negative interaction potential is scaled
such that its range and its scattering length are both of order
$(N/\varepsilon^2)^{-1}$, corresponding to the Gross-Pitaevskii scaling of a
dilute Bose gas. We show that in the simultaneous limit $N\rightarrow\infty$
and $\varepsilon\rightarrow 0$, the dynamics preserve condensation and the time
evolution is asymptotically described by a Gross-Pitaevskii equation in one
dimension. The strength of the nonlinearity is given by the scattering length
of the unscaled interaction, multiplied with a factor depending on the shape of
the confining potential. For our analysis, we adapt a method by Pickl to the
problem with dimensional reduction and rely on the derivation of the
one-dimensional NLS equation for interactions with softer scaling behaviour.
