▲promise可以接双宾语：promise you a chance，“答应给你一个和机会”。

▲whoever是一个复合连接代词，意思相当于anyone who, any person who.一词兼两职，既充当了先行词，又充当了关系代词，可以充当从句的主语。而whomever意思相当于anyone whom, any person whom.不能充当从句的主语，只作宾语。

所以你给的句子，实际是：

We promise whoever attends the party a chance to have a photo taken with the movie star.

= We promise anyone who attends the party a chance to have a photo taken with the movie star.

▲不定式to have a photo taken with the movie star作a chance的定语。