Efforts to broaden participation in computing have led to gender-focused interventions intended to increase the number of women in the field of computing. However, such efforts have failed to significantly increase the percentage of Black women in computing. For example, only 1% of the 28,884 bachelor's degrees in computing were awarded to Black women in 2018. Moreover, too few empirical studies have intentionally explored the lived experiences of Black women, an often overlooked and understudied population in the computing ecosystem. In this paper, we introduce intersectionality - the complex overlap of socially constructed identities such as race, gender, class, sexuality, etc. - as a theoretical framework and springboard for exploring the lived experiences of Black women in computing. We interview 14 Black women in various stages of the computing ecosystem (undergraduate students, graduate students and early career professionals) to understand how intersectionality influences their ability to persist in computing. Preliminary findings from the analysis of the 14 interviews provides insights into how the interlocking systems of oppression (i.e., gendered racism) play out in computing education and negatively impact the recruitment and retention of Black women in the field of computing.