Chichi no Jikan follows Shinogi Kyuuichi, a male biology student who lives in an apartment near a helpful female neighbor/friend, Takarai Ayaka. One day, he is visited by aliens, who demand that he raise their baby for a year... or else the world is history. The baby is apparently human, and is raised the way humans are: through breast-feeding. Kyuuichi's sex is not a problem for the aliens: they give him a simple device that switches his body to a woman's with the mere touch of a button. Conveniently, Kyuuichi's female form is very well-endowed.
Although she's understandably confused and uncomfortable by the whole situation, Ayaka helps Kyuuichi out as he navigates the unfamiliar experience of raising a child, and breast-feeding it in particular. That means going to a store to buy a breast pump, visiting a maternity hospital to get a massage to release Kyuuichi's stored-up milk, and giving the baby a bath together. Kyuuichi, as a biology student, is fascinated by the whole thing from an academic perspective.