The phrase "chronicle small beer" means to write about unimportant or trivial matters. Synonyms for this phrase include "record minutiae," "note trivia," "document inconsequentials," "jot down details," "report minutiae," and "memorialize trivialities." These expressions all convey the sense of paying attention to minor, unimportant details, and could be used in a variety of contexts, such as in literary criticism, historical research, or journalism. Whether describing the habits of a minor character in a novel, chronicling the daily routines of a famous figure, or writing an article about a little-known event, these synonyms all capture the idea of focusing on the small things that can add up to a larger picture.