。
Please forgive me for breaking the promise.
Literal
Promise [obj-を] broke thing [obj-を] forgive-[request-てください].
The pattern [past-form verb]+事を+許す treats the past action itself as the object of forgiveness — 'forgive the fact that I broke it.' 事 is written in kanji here where こと would be more standard in modern writing; the kanji form is slightly heavier, more formal in feel. A straightforward apology.