Leave it to the 21st century to make an animated film about a classic children’s story character and add Freudian subtext. In “Chicken Little,” Disney’s latest CGI offering, the diminutive title character must not only save the world by convincing his town that the sky is indeed falling, but also grapple with feelings of loneliness, desperation and inadequacy (whew).

The movie begins where the fairy tale originally left off: Chicken Little (Zach Braff), infamous for having incited chaos in the town of Oakey Oaks with his false alarm that the sky was falling, is all but shunned by society for his blunder. The only real attention he does receive is entirely negative — as the town is soon inundated by a storm of media coverage in the form of books, books on tape, board games, billboards, bumper stickers and collectible souvenir spoons. Even Chicken Little’s own father, former baseball star Buck “Ace” Cluck (Garry Marshall), treats him with condescension and embarrassment.

“Just lay low,” he tells his son. “It’s like a game of hide-and-seek, only the goal is never to be found, ever.”

As a result, Chicken Little is quite the disturbed fowl, and Braff’s near-neurotic reading is already suggestive enough on its own. A tiny, bespectacled student at an elementary school attended mainly by animal characters from other fables, the chicken’s closest friends are other outcasts like Fish Out of Water and Abby “Ugly Duckling” Mallard (Joan Cusack).

Trying to stand up to a bully one day in gym class, Chicken Little declares, “Prepare to hurt, and I don’t mean emotionally, like I do.” The line definitely seems a bit out of place in a children’s movie, unless the producers had a certain Victorian boarding school demographic in mind.

Granted, after movies like “Toy Story” and “Shrek,” infusing family films with a little adult flavor is nothing new. But when animated characters start talking about the need for “closure” in parent-child relations (as Abby does), one begins to wonder at whom, exactly, the material is directed. At certain times, “Chicken Little” feels less like an actual film and more like either self-help for parents or feel-good medicine for kids.

Unfortunately, the most substantive elements of the movie seem so trite they could have been made by, well, a computer. The plot unfolds at first rather predictably, then downright clumsily, then wheels back to predictable again, as Chicken Little takes up baseball to prove himself to his father, succeeds and then must fend off an alien invasion when the sky really does start falling.

Not that “Chicken Little” is entirely without its charms. Perhaps the most fun to be had is in discovering just how many different celebrities lent their voices to the computer-animated barnyard menagerie. In addition to Steve Zahn, who executes a hilarious rendering of the rotund, Barbara Streisand-collecting pig named Runt of the Litter, the movie features Patrick Stewart, Don Knotts, Wallace Shawn, Fred Willard and Catherine O’Hara. A minor highlight — and maybe the biggest laugh of the film — is when Harry Shearer lends his Kent Brockman-esque deadpan to the radio commentator dog who narrates Chicken Little’s baseball game. After a brutally slow swing and miss, the announcer intones seriously, “Ladies and gents, I’m not going to sugarcoat it: I’ve seen roadkill with faster reflexes.”

Ultimately, “Chicken Little” fails to do what other, more successful CGI movies have done so well: create an entirely original, self-sustained alternate universe in which the characters can live and breathe effortlessly. “Shrek” showed us a world of fairy tales come to life and exploited the comic potential therein. Likewise, “Finding Nemo” imagined a whole underwater civilization. “Chicken Little” borrows something from “Shrek,” something from real life and the rest from all over the map. Much like its title character’s notorious proclamation, the movie may just be a bit too much to be believed.