。
She kept the secret entirely to herself.
Literal
She [topic-は] that secret [object-を] own [genitive-の] chest one-alone [in-に] kept-hidden-left-it.
胸ひとつに秘める is an expressive set phrase: 胸 ('chest, heart') + ひとつ ('one alone') + に ('in') + 秘める ('hide, conceal') — literally 'kept it hidden in just one chest,' meaning 'kept it entirely to oneself, told no one.' The 自分の at the front intensifies the solitude. ~ておく adds the nuance of keeping the state in place — the secret is being deliberately maintained as undisclosed. Compared to plain 秘めた ('concealed'), the おく flavor is 'left it that way, on purpose.'