  In this note we introduce the poset of $m$-multichains of a given poset
$\mathcal{P}$. Its elements are the multichains of $\mathcal{P}$ consisting of
$m$ elements, and its partial order is the componentwise partial order of
$\mathcal{P}$. We show that this construction preserves a number of
poset-theoretic and poset-topological properties of $\mathcal{P}$. Moreover, we
describe the structure of the poset of $m$-multichains of a finite distributive
lattice, and provide a link to R.~Stanley's theory of $\mathcal{P}$-partitions.
