  We study the emergence of odd-frequency superconducting pairing in UPt$_3$.
Starting from a tight-binding model accounting for the nonsymmorphic crystal
symmetry of UPt$_3$ and assuming an order parameter in the $E_{2u}$
representation, we demonstrate that odd-frequency pairing arises very
generally, as soon as inter-sublattice hopping or spin-orbit coupling is
present. We also show that in the low temperature superconducting $B$ phase,
the presence of a chiral order parameter together with spin-orbit coupling,
leads to additional odd-frequency pair amplitudes not present in the $A$ or $C$
phases. Furthermore, we show that a finite Kerr rotation in the $B$ phase is
only present if odd-$\omega$ pairing also exists.
