Hadhrat Hudhayfah (may Allaah be pleased with him) and his father Hadhrat Yamaan (may Allah be pleased with him) were on their way to Madinah to meet with Rasulullaah (peace be upon him) when Abu Jahal got hold of them.
When he asked them where they were headed, they informed him that they intended to meet Rasulullaah (peace be upon him) in Madinah.
He had placed a sword to their necks and they had to make the promise to save their lives. Hadhrat Hudhayfah (may Allaah be pleased with him) therefore asked Rasulullaah (peace be upon him) to allow them to fight in the battle because their promise was one made under threat.
We learn from this incident that even if a promise is made to a Kaafir (non believer), it must be kept as far as is possible. However, there may be different situations at different times that will not be like this.
It is therefore necessary to always ask the Ulema (Scholars of Islam) and the elders whenever such occasions arise.