Finally bothered to track it down, and yep, it's a still from Billy's turn as the malevolent little kid with God-like powers (and the family who loves him) in the 1961 Twilight Zone episode, "It's a Good Life."
You've probably seen it, or know the story, but here's six-plus minutes of highlights anyway.
Still pretty creepy.
Inevitably I ended up at the wiki for the episode. Interesting, he averred weakly, especially the paragraph about the 2008 theatrical adaptation of the original short story, which notes that the play included some new scenes, in one of which
Anthony's [the mean widdle god's] mother apologizes [to a neighbor and his boy] for "what happened to your dog." The boy responds, "Yes, it was good that Anthony made Jasper choke to death eating his own paws."
Now that's playwritin'! Suck it, Serling! After that, the paragraph can only end lamely:
Also, Dan Hollis kills himself with shards of his birthday record rather than Anthony transforming him into something awful.