  A perfect $K_r$-tiling in a graph $G$ is a collection of vertex-disjoint
copies of the clique $K_r$ in $G$ covering every vertex of $G$. The famous
Hajnal--Szemer\'edi theorem determines the minimum degree threshold for forcing
a perfect $K_r$-tiling in a graph $G$. The notion of discrepancy appears in
many branches of mathematics. In the graph setting, one assigns the edges of a
graph $G$ labels from $\{-1,1\}$, and one seeks substructures $F$ of $G$ that
have `high' discrepancy (i.e. the sum of the labels of the edges in $F$ is far
from $0$). In this paper we determine the minimum degree threshold for a graph
to contain a perfect $K_r$-tiling of high discrepancy.
