  Let $X$ be a smooth threefold with a simple normal crossings divisor $D$. We
construct the Donaldson-Thomas theory of the pair $(X|D)$ enumerating ideal
sheaves on $X$ relative to $D$. These moduli spaces are compactified by
studying subschemes in expansions of the target geometry, and the moduli space
carries a virtual fundamental class leading to numerical invariants with
expected properties. We formulate punctual evaluation, rationality and
wall-crossing conjectures, in parallel with the standard theory. Our formalism
specializes to the Li-Wu theory of relative ideal sheaves when the divisor is
smooth, and is parallel to recent work on logarithmic Gromov-Witten theory with
expansions.
