Internationally, there is widespread concern about the need to increase participation in the sciences (particularly the physical sciences), especially among girls/women. This paper draws on data from a five-year, longitudinal study of 10-14-year-old children's science aspirations and career choice to explore the reasons why, even from a young age, many girls may see science aspirations as "not for me". We discuss data from phase one--a survey of over 9000 primary school children (aged 10/11) and interviews with 92 children and 78 parents, focusing in particular on those girls who did not hold science aspirations. Using a feminist poststructuralist analytic lens, we argue that science aspirations are largely "unthinkable" for these girls because they do not fit with either their constructions of desirable/intelligible femininity nor with their sense of themselves as learners/students. We argue that an underpinning construction of science careers as "clever"/"brainy", "not nurturing" and "geeky" sits in opposition to the girls' self-identifications as "normal", "girly", "caring" and "active". Moreover, we suggest that this lack of fit is exacerbated by social inequalities, which render science aspirations potentially less thinkable for working-class girls in particular. The paper concludes with a discussion of potential implications for increasing women's greater participation in STEM (Science, Technology, Engineering and Mathematics). (Contains 2 tables and 6 notes.)