You don't expect to see an alligator strutting its stuff on a residential sidewalk, but that's what happened in South Carolina ... and a poor woman almost ran right into this thing!

Check out this wild footage ... it shows a rogue croc casually chillin' right in front of a person's home in Hilton Head Island Wednesday before the owner innocently strolls along with her dog ... completely oblivious to the scaly surprise waiting for her.

She actually gets within inches of the gator before finally noticing it -- she wasn't even on her phone, BTW, so it's crazy that she didn't see it -- it scares the bejesus out of her.

The woman flinches so hard when she spots the reptile that even her dog gets spooked -- and the scaly beast wasn't too thrilled about the sudden commotion either. It immediately opens its mouth and hisses ... looking ready to go into attack mode!

The woman falls flat on the ground in shock ... but after bouncing back up, she bolts a little distance before looking back to confirm what she's actually seen. Her panicked cries cause such a scene that it draws other neighbors out of their homes ... and you can hear them chatting about the gator off-camera.

A dude is also heard trying to connect the dots ... asking the woman if she's got some kind of creek or body of water on her property that the gator's trying to get to. All this happens as the gator makes a move ... casually sauntering into her greenery like it owns the place.

Turns out, the gator's field trip might not be as surprising as it seems, as sources tell TMZ there's a pond only 5 minutes from this location ... which is probably where it came from.

We're also told that the gator wasn't done with its little tour of the neighborhood. It made a comeback around 5 PM, this time ending up in the neighbor's backyard ... watch the footage.

Luckily, it didn't stick around for too long -- vanishing into thin air once again ... and not harming anyone or anything. Animal control wasn't called during the whole thing, FWIW.