I’ve watched Chobits years ago and was curious.
The first episode/chapter tells us about how Hideki found Chii in the dumpster.
According to the plot description in the Wikipedia article Chobits (bold emphasis mine):
The series centers on the life of Hideki Motosuwa, a held-back student attempting to qualify for university by studying at Seki prep school in Tokyo. Besides a girlfriend, he dreams of having a persocom (パソコン?): an android used as a personal computer, which is expensive. On his way home one evening, he stumbles across a persocom in the form of a beautiful girl with floor-length hair lying against a pile of trash bags, and he carries her home, not noticing that a disk fell on the ground. Upon turning her on, she instantly regards Hideki with adoration. The only word the persocom seems capable of saying is "chi" (ちぃ Chii?), thus he names her that.
What does the disk contain?