。
She happened to know his address.
Literal
She [topic-は] by-chance his address [object-を] [knew-知っていた].
たまたま is the everyday adverb for 'by chance, as it happened, coincidentally' — used to flag an outcome that wasn't planned or expected. 知っている is the resulting-state form of 知る ('come to know'); plain 知る denotes the moment of acquiring knowledge, while 知っている describes the lingering state of being someone who knows. Here in past tense 知っていた, it locates the knowing in the past — 'she was already in possession of his address (when whatever happened, happened).' This stative reading of 知る is one of the canonical examples taught with ~ている.