  Given positive integers $a\leq b \leq c$, let $K_{a,b,c}$ be the complete
3-partite 3-uniform hypergraph with three parts of sizes $a,b,c$. Let $H$ be a
3-uniform hypergraph on $n$ vertices where $n$ is divisible by $a+b+c$. We
asymptotically determine the minimum vertex degree of $H$ that guarantees a
perfect $K_{a, b, c}$-tiling, that is, a spanning subgraph of $H$ consisting of
vertex-disjoint copies of $K_{a, b, c}$. This partially answers a question of
Mycroft, who proved an analogous result with respect to codegree for
$r$-uniform hypergraphs for all $r\ge 3$. Our proof uses a lattice-based
absorbing method, the concept of fractional tiling, and a recent result on
shadows for 3-graphs.
