。
She has a chronic illness.
Literal
She [topic-は] chronic illness [to-に] is-afflicted.
慢性の病気にかかっている — 慢性 (まんせい, 'chronic') is a medical term. 病気にかかる ('to catch/contract a disease') is a standard medical expression. ている marks the ongoing state.
。
She has a chronic illness.