Is there a known technique for giving your readers chills?

For just about any communication, the connection to the emotional(physical) level -- to give the reader chills -- is made through lighter emotional connections. To read the level of Immersion, as it is also called -- that place where frisson and sensory experiences -- requires clear writing, but not plain. Emotional without being purple and soggy.

...and the use of the emotional experience in description, narration, and dialogue if you can fit it in without sounding silly. Want feelings of alarm, use metaphors in clusters that hint at missing out on something or not getting some desire fulfilled.

Find and read a paper titled "Spiderman? Sure!" for more information and leads to this area. Also, search out and explored VADs (Valence, Arousal, Dominance). Also, the book Predictably Irrational.

Words have power, and there are lists of powerful words out there.

But even in the mild vocabularies, words have power. Like yawn. Yawn isn't a command or even a verb. No one is yawning in front of you, so this is fiction. It's good. Yawn is the name of an action, a common event; mundane, easy, safe. Yawning happens all the time. Yawning isn't even a discomfort. Some people like to yawn. So, yawn offers no threat, no cohesion, nothing. Yet, when one person yawns, other people yawn. It happens. There is no, why. It just happens, and when yawning people spread their yawns on the page, you don't have to see them, do you?

No, you don't. You'll yawn in an empty room, just like we were all there together. Just as your emotions are with you now, and it's a wonder that this is questioned, when you have never had a moment, the space of an inhale, in which you did not have a correlating emotional response.

I hope this helps so many years later.

Well, according to Emily Nusbaum and Paul Silvia of the University of North Carolina (the authors of one of the most significant studies about 'music chills'), the response might depend on your personal history and 'the way you are'.

Musical chills, write the authors, are "sometimes known as aesthetic chills, thrills, shivers, frisson, and even skin orgasms [who knew?] … and involve a seconds-long feeling of goosebumps, tingling, and shivers, usually on the scalp, the back of the neck, and the spine, but occasionally across most of the body." The scientific explanation for chills is that the emotions evoked by beautiful or meaningful music stimulate the part of the brain called the hypothalamus, which controls primal drives such as hunger, sex and rage and also involuntary responses like blushing and goosebumps. _Source

So music ones appear to be related not only to the emotions you evoke while listening to it but also to your personality:

They also measured their experience with music, and five main dimensions of personality: extraversion, conscientiousness, agreeableness, neuroticism, and openness to experience. Of all these dimensions, only openness to experience was related to feeling chills. People high in openness are creative, curious about many things, have active imaginations and like to play with ideas, and they much more frequently feel chills in response to music._Source

Apparently, people that were more 'open to experiences' were also more likely to play a musical instrument themselves (they rated music as more important in their lives than people low in openness). I guess this makes the experience of music a bit more personal.

The same thing might be applied to reading. The more involved you are with what you're reading, and the more you use your imagination and relate to the story with respect to your personal life, the easier it will get to feel those chills.

Ultimately it seems to depend on the reader and his/her relationship with your book. However, if you can create vivid images that relate to universal human experiences, chills shouldn't be a problem for your sensitive readers :)

An excellently executed Hidden in Plain Sight (warning: TVTropes link!) is a surefire trigger.

Specifically: A deeply disturbing, truly scary thing which was the proverbial elephant in the room, executed well enough that the reader failed to notice it despite obvious hints. It was a menace capable of striking at any moment, stabbing our exposed backs from the middle while we stood in a circle looking outside for the danger. Maybe it did strike unnoticed a few times already, and we always boggled who or what caused it while the murderer was standing right next to the victim. It loomed at all times, feeling creepy but forgotten as a mood-building background element. Only when we reach a resolution, when we lost our primary defenses and stand exposed, vulnerable and desperate, learning long-overdue secrets, our cocky approach long snuffed, us doing our homework of research diligently, at last, we read the page that identifies our menace, and we realize it reads it over our shoulder with us, as it kept doing for past half an hour.

This is the moment that sends a deep cold shiver down any reader's spine.

I think there's no specific formula. If your story gives you the chills, then it will give the chills to your readers too (or at least, it will increase the probability).

Now coming up with an idea/story that does that is another thing. I think it is different for everyone. But in theory, if you read authors that give you the chills, and try to emulate (or take inspiration from them), you'll eventually write something that produces the same effect.

The thing I do is to come up with as many ideas/stories as possible. I don't know you, but ideas pop up in my mind all the time. While jogging, taking a shower, watching a movie, taking a dump, etc. And I write them all, even the ridiculous ones (I don't necessarily finish them)—then I wait. I leave them there for a couple of months. Then I come back to them. And if the story still gives me the chills, I keep working on it. It means it survived the test of time. Natural selection.

So to conclude, there's no specific formula. The best you can do is to try as many ideas as you can and pick those that "survive." If they really give the chills, they won't be defeated by the passage of time.