Ok, now I'll actually post some songs.
You could really post nearly every Modest Mouse song from their first 3 ... Dramamine, Tundra and Desert, Ohio, Talking Shit About A Pretty Sunset, Make Everyone Happy/Mechanical Birds, Teeth Like God's Shoeshine, Heart Cooks Brain, Cowboy Dan, Trailer Trash, Truckers Atlas, Bankrupt on Selling, Styrofoam Boots, 3rd Planet, A Different City, The Cold Part, Alone Down There, The Stars are Projects, A Wild Pack of Family Dogs and Lives. But THIS is probably the best one.
Pretty much everything on this entire album, to be honest.
I think if we're talking about the classic definition of songs that give you chills, then these 3 are probably the most classic examples in history:
This is a pretty poppy example but a very good one, too:
And if we're talking about songs that give you chills because of the movie they're in, then this is a prime candidate:
Although honestly, I'm pretty sure the actual song is more chilling than the entirety of Silence of the Lambs ....
If you want to see a chilling example of possibly the most depressing mindspace ever, that truly makes you think about humanity in the deepest of ways, this is a good choice:
And of course, you can't make a list of songs that give the chills without post-punk!!!
It's very arguable that no song can communicate what this song tries to communicate, as well as it.
If you want to meme and cry at the same time:
And of course, TRUE David Bowie fans know that his most chilling song is not the Man Who Sold the World, but The Bewlay Brothers!:
Okay but seriously, last of all, if we're talking about chills given from nostalgia and the passing of time, then this is a good pick:
It's a happy song, and I barely heard it as a kid, but it definitely seemed like it was in every commercial back in the mid 2000's (and probably some shitty youtube vids too)