One day in Academy (two years before graduation?), Sasuke is feeling particularly angry (because it's the anniversary of the Massacre?). When Sakura asks him for a date, he snaps: "Do you know what I hate? I hate weak ninja—and you are a weak ninja. I've seen you, flailing worthlessly in sparring—panting with exhaustion after making three simple Clones—whispering with the others about hair and diets instead of practicing shurikenjutsu. Don't even talk to me until you can see my level from the bottom of the ravine that you're stuck in… weakling."
Sakura is the only person who hears this one-in-a-million outburst. She resolves to train up her taijutsu and shurikenjutsu, as instructed—but she's at a loss in the area of chakra. Research at the library turns up a yellowed scroll containing the Harmonious Flow Technique—a simple precursor of the Mystical Palm, meant only to transfer chakra from the medical ninja to the patient (e. g., to remedy a case of chakra exhaustion). Sakura hypothesizes that forcing extra chakra into a person with a full reserve will stretch the maximum capacity of that reserve over time. To that end, she promises to go on some dates with Naruto after he learns Harmonious Flow (and the average-level chakra control necessary to use it) and helps her to train in taijutsu and shurikenjutsu.
Sakura's hypothesis is correct, and the size of her chakra reservoir starts to increase dramatically after Naruto gets the hang of forcing his medically-sterilized chakra into her system. (She also greatly improves her shurikenjutsu and taijutsu, helping Naruto to cover his areas of weakness as well.) However, there's a side effect to the Harmonious Flow Technique. Like most medical techniques, it causes a soothing, mildly-anesthetic pleasure for anyone on whom it's used—but the "reservoir-stretching" feeling inflicted on a target with already-full reserves is particularly intense. Sakura finds herself addicted to the euphoria.
I don't know where the story would go from there. Maybe Sakura's addiction would be discovered by Iruka or Mizuki, solidifying the necessity of having them on the same team, despite Naruto's improved grades. It definitely would involve some delicious descriptions of Sakura's anticipations of, and reactions after, the chakra infusions, though…
Explanation of mechanics: Every person's chakra network is a self-repairing balloon. When that balloon is stretched by an infusion of chakra beyond its normal capacity, it develops thicker skin in order to maintain a constant safety margin of strength. An older person's chakra network has less of this self-repair capability.
Alternate path: A few hours after the first infusion of chakra, Sakura realizes that this very well could be addictive—and, obviously, there's no point in getting addicted to Naruto if she wants to get into Sasuke's good graces. She decides to conduct experiments in order to determine whether or not the same euphoria is produced in other combinations of people. What is its cause? Is it big chakra vs. small chakra? Male vs. female? Naruto's chakra nature vs. her chakra nature (whatever they may be)? Hinata and Chouji are first in line to be recruited for such efforts, since they can be trusted to keep secrecy. (Shino would be in there as well, but his nonstandard body might affect the results.)
Alternate explanation of mechanics: A person with large chakra reserves has in his soul a larger "hole" leading to the "chakra dimension" (source of all chakra, at constant "pressure" throughout). A person who repeatedly drains his chakra to the bottom lowers his internal chakra pressure, causing the chakra to "flow" into him at a higher speed and thereby increasing the erosion of the "edge" of his chakra hole. However, that doesn't work with this story idea.