Vow
Oath
This looks like an adjective, but it's actually a noun. This word is the same as the kanji meaning: vow (or oath).
ちかい
This has the same reading as 近い (ちかい). Just think about how when you're making a vow or oath, you become closer to the thing or person you're vowing to. You belong to them, in a way, which is why you become close (近い).
結婚の誓いの言葉を述べている時、自分が間違った男の人と結婚しようとしていることは分かっていました。
When I was saying my wedding vows I knew I was marrying the wrong man.