She didn’t realize that she was addicted to nicotine until she had smoked ten cigarettes a day.

This is because the past perfect tense "had smoked" is used to show that the smoking occurred before the realization. So, her smoking ten cigarettes a day happened first, and her realization of being addicted happened later.

Both sentences are grammatically correct, but they emphasize different sequences:

"She hadn’t realized that she was addicted to nicotine until she smoked ten cigarettes a day."

This suggests that the lack of realization (not knowing she was addicted) continued until she reached the point of smoking ten cigarettes. The not-knowing came first.
"She didn’t realize that she was addicted to nicotine until she had smoked ten cigarettes a day."

Here, the past perfect "had smoked" clarifies that she smoked the cigarettes before her realization.