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 :)