Sort archives by category

I’m trying to figure out how to arrange the archives on my site by category, to look something like this:

Category Name
Post name/link
Post name/link
Post name/link

Category Name
Post name/link
Post name/link
Post name/link

Category Name
Post name/link
Post name/link
Post name/link

Time and date are irrelevant for this particular site – it’s a collection of stories written by upwards of 30 people relating to a missions trip, and each person is going to be posting their stories to their own category.

I searched the forums for a solution but couldn’t find one. Is there a tag or plugin that would help me arrange my archives like this?