The applicability of copyright law does *not* depend on whether you charge for admission or make money off the showing of the work. Many people think it does; that's simply wrong. (Whether and how much you charge *does* affect the *damages* that the plaintiff can ask for in court, but that's different.)

Whether or not you're charging is one of the 4 factors that determine whether a particular use is "fair", but only a federal court can decide whether any particular use is "fair". (The other 3 factors are the nature of the work, the amount you use, and the effect of your copying on the potential market for the work. So even if you're not charging, but you are affecting the potential market, your copying is very likely *not* fair use.)

The U.S. Copyright Office has a fair-use summary that you should read -- it has a list of several uses that are known to be fair; see the section beginning with "The 1961 Report of the Register of Copyrights on the General Revision of the U.S. Copyright Law". This is not an exhaustive list I don't think, but anything sufficiently similar to this should be OK.

In this case, where nix is considering using a single frame of a movie, the amount of the work that's being used is positively tiny. (1 frame out of a couple hundred thousand.) The item out of the list in the linked-to article that may apply is "reproduction by a teacher or student of a small part of a work to illustrate a lesson" -- if it's being used to illustrate anything. The other item that may apply is "quotation of short passages in a scholarly or technical work, for illustration or clarification of the author's observations", if (again) it's being used for illustration.

My guess is that it might be fair use, but I am most definitely not a lawyer. (My guess is based on mostly the amount of the movie that's being used, and the sort-of similarity to the items I posted above; not the money being charged or not being charged.)

nix -- Talk to a lawyer. Or better yet, it might be possible to talk to whoever published the movie; perhaps they'd just let you use the one frame. Getting permission is always better than assuming it's fair use, then getting slapped with a lawsuit when the author disagrees.

(Then again, this is the MPAA we're talking about -- no matter how little you used, they probably wouldn't agree that it was fair use until you proved it in court. Blech.)