She had him chop firewood.

Literal

She [topic-は] him [to-に] firewood [object-を] made-split.

A causative construction: 割らせる (causative of 割る 'split, break'). The causee (the person made to do the action) takes に here — but in causative constructions, the causee's case-marking depends on the verb's transitivity: with intransitive verbs, the causee can take either に or を; with transitive verbs (like 割る, taking まきを), the causee takes に. So we get 彼にまきを割らせる — 'made him split the firewood,' two different things marked by に and を.