What is the first occurence of film within a film within a film?

Spaceballs (1987) has this scene, in which the villains watch... Spaceballs, including the scene they're currently in. Even at YouTube image quality, you can see at least three levels on the screen — and, of course, the number of implied levels is infinite.

(The two-level version shows up as early as Buster Keaton's Sherlock, Jr. (1924), so I'm sure there's a three-level example earlier than this, but it's the best I've been able to think of so far...)

R?kopis znaleziony w Saragossie (English title: The Saragossa Manuscript) (1965) is the earliest example that comes to mind:

The maximum depth of nesting of the story is Fraquita's tale, which begins in Q-2-j-(1)-(a). If we see Alfonso's experiences as all being at a single level, that makes The Saragossa Manuscript a story-within-a-story having seven levels: counting Has' movie as level one because it is a presentation of Potocki's novel (level two) that tells about two opposing army officers sitting together and reading Alfonso's book (levels three through seven, or a subtotal of five levels). (Source)

It's a while since I saw this film and my recall of it is imperfect, but my recollection is that in the sense that the sub-levels are essentially short films intercut, in nested fashion, into the level one film, there is indeed a film within a film within a film here.

However, if instead "film within a film within a film" refers to the presence in the main film of some other narrative on a moving picture screen, that depicts in turn some other narrative on some moving picture other screen, then no, there isn't.

Probably not the first, but it definitely precedes Scream 4::

Rosencrantz & Guildenstern Are Dead (1990), by Tom Stoppard, based on his own play from 1966.

• In one scene

  Rosencrantz and Guildenstern come upon The Player and The Tragedians as they rehearse the dumbshow for their production of The Murder of Gongazo.

  What we eventually see is

  a film version of a puppet show within a dumbshow within a rehearsal for a play-within-a-play that is made up primarily of the backstage parts of another play.

• or, to say it differently:

  It's basically 'Hamlet' within 'Hamlet' within 'Hamlet'... within 'Rosencrantz and Guildenstern are Dead'... which is within 'Hamlet'.

The beginning of horror film Killer Party (1986) is one of those, and actually very similar to Scream 4.

It starts at a funeral. The mourners leave while the daughter, happy that her mom died, sticks around to hurl insults at the coffin when she's suddenly attacked by the corspse, get trapped inside the coffin and then burns alive when it's cremated.

This then turns out to be a movie, that a girl and her boyfriend are watching at a drive in theater. The girl goes to get some popcorn, comes back and is attacked by her boyfriend who's now a zombie.

But this also turns out to be a short film\music video called "You're No Fool" and centered around horror tropes and April Fools, that the actual movie's heroine is watching on TV.

So it's a surprisingly similar structure, and came out 25 years before Scream 4. It's also a blatant... let's say homage to Michael Jackson's classic Thriller video from 1982 (which you can see here).

One example is Austin Powers in Goldmember (2002):

In a self-parody of the Austin Powers series, there is a film within the film in the opening. Austin Powers is featured in a bio-pic called Austinpussy (a parody of the James Bond film Octopussy) directed by Steven Spielberg and starring Tom Cruise as Austin Powers, Gwyneth Paltrow as Dixie Normous, Kevin Spacey as Dr. Evil, Danny DeVito as Mini-Me, and John Travolta as Goldmember.

And at the end:

The heroes arrest Goldmember, who turns to the camera to reveal the entire string of events was adapted into a film by Steven Spielberg, starring Tom Cruise as Austin, Kevin Spacey as Dr. Evil, Danny DeVito as Mini-Me, and John Travolta as Goldmember. Austin, Foxxy, Dr. Evil, Mini-Me and Nigel are in the audience of a Hollywood theater watching the film.

You may also be thinking of Scream 2 and 3 (1997 and 2000), which although weren't examples of a film-within-a-film-within-a-film, each had a film-within-a-film:

In the latter two films of the Scream horror trilogy, a film-within-a-film format is used when the events of the first film spawn their own horror trilogy within the films themselves. In Scream 2, characters get killed while watching a film version of the events in the first Scream film, while in Scream 3 the actors playing the trilogy's characters end up getting killed, much in the same way as the characters they are playing on screen.

Boogie Nights: In Dirk's first role, he plays an actor auditioning for a part in a film.