。
You must vow to keep your promise.
Literal
Promise [obj-を] keep-[nominalizer-こと][obj-を] swear-[must-なければいけない].
Stacks ~ことを with 誓う, nominalizing the first clause ('keeping the promise') as the direct object of 'swear.' The obligation is expressed by ~なければいけない, one of the main 'must' patterns — literally 'if-not [doing] is no good.' A deeply layered sentence that is more forceful than it needs to be for its content.