I’ve heard this phrase, and variants thereof, fairly often - particularly in cartoons.
What it means is obvious - ‘Run for it, the authorities are here!’ - but how the heck ‘Cheese it!’ came to mean ‘Run!’ rather escapes me.
Anyone know the origin of the phrase?
“Cheese it” doesn’t mean “run”, it’s a euphemism for “Jesus Christ” and the intended meaning is “dammit!”.
It is cited in print as far back as 1811. It was underworld slang for “keep quiet.” (instantly)
There is quite a bit of criminal slang that was meant to be ‘mysterious’ to average people who overheard it. Sort of code. I’m not saying that is the case, but it could have been.
Alas, for now, it’s “origin unknown.”
Well, that certainly makes sense.
That’s the theory I’ll stick with, even if ‘theory’ is the best we can do.
Also known as argot.
Oh please. Doesn’t anyone take pictures any more?
“Cheese it” = smile the way you do when someone’s taking your picture and tells you to say “cheese”, i.e., look pleasantly innocent here come the cops.
Oh, please, yourself. You’re just making that up, right? If samclem’s 1811 date is right, it can’t possibly have anything to do with photography.
I’ve always heard and read it to mean exactly what the OP said, and only what he said: run for it. (So I disagree with AndrewT, too.)
What’s your source, samclem?
I think AHunter is having us on, commasense.
“Cheese it” in the contested phrase is a reworking of “Cease it”, i.e. stop what you’re doing.
It’s derived from “cut the cheese” which is to fart. When the cops are coming after you, you should let off the smelliest fart possible so that the cops fall ill and stop chasing you. 
All right, you big crazies. :smack:
From Dictionary.com:
No, no, no, no, no! It comes from Wales and it is based on their national dish ‘Welsh Rarebit’ or cheese on toast. ‘Cheese it’ simply means to act like the cheese under a grill. Melt. Melt away into the night from the cops. Like cheese.
My husband, the Geezer in Training, always says, “Chiggers! The fuzz!” Slight hijack, but it cracks me up every time.
Well then, with the OP more or less answered, and summer coming on, this seems like the perfect time to mention the highly entertaining sport of Cheese Racing.
Well if things are gonna get cheesetastic the I’ll see your ‘cheese racing’ and raise you the ultra dangerous cheese tolling. I recommend googling 'cheese rolling and looking for more pictures, I’ts very psycho.
‘rolling’ not ‘tolling’. Now that link wasn’t the one I wanted this is the one I wanted to show you. Go down about a third of the way down the page and click in the ‘seeing is believing’ section coloured blue to start the picture gallery.