Women experience chronically inferior returns in organizations. One common recommendation is to form instrumental network ties with high-status others in groups. We integrate research on social status, social perceptions, and gender issues in social networks to suggest that, despite the theoretical and empirical appeal of this approach, instrumental ties to high-status network contacts (versus ties to lower-status network contacts) in groups may incur hidden social status costs for women in intragroup status-conferral processes. Instrumental ties to high-status network contacts may be perceived as a sign of agency of the focal person, which violates feminine gender norms. Women with these high-status network contacts in groups may therefore be perceived as less communal, thus subsequently lowering their status in the eyes of other group members compared with women with lower-status network contacts. Studies 1–4, across cross-sectional, longitudinal, and experimental designs, support our model. Study 5 suggests that signaling a group-oriented goal may mitigate the interpersonal, social perceptual costs of instrumental ties to high-status network contacts for women. The effect of ties with high-status network contacts for men is relatively inconsistent. This research reveals a potential social-network dilemma for women: Instrumental ties to high-status network contacts in groups and organizations are necessary for success and should be encouraged, yet they may also create an extra social perceptual hurdle for women. Organizations need to investigate social and structural solutions that harness the benefits of high-status network contacts for women, while minimizing any potential social perceptual costs. Funding: Financial support from the Jones Graduate School of Business, Rice University, is gratefully acknowledged. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/orsc.2020.14640 .