  Given graphs $F$ and $G$, a perfect $F$-tiling in $G$ is a collection of
vertex-disjoint copies of $F$ in $G$ that together cover all the vertices in
$G$. The study of the minimum degree threshold forcing a perfect $F$-tiling in
a graph $G$ has a long history, culminating in the K\"uhn--Osthus theorem
[Combinatorica 2009] which resolves this problem, up to an additive constant,
for all graphs $F$. In this paper we initiate the study of the analogous
question for edge-ordered graphs. In particular, we characterize for which
edge-ordered graphs $F$ this problem is well-defined. We also apply the
absorbing method to asymptotically determine the minimum degree threshold for
forcing a perfect $P$-tiling in an edge-ordered graph, where $P$ is any fixed
monotone path.
