Killing by cytotoxic T lymphocytes (CTLs) is mediated by the secretion of lytic granules. The centrosome plays a key role in granule delivery, polarizing to the central supramolecular activation complex (cSMAC) within the immunological synapse upon T cell receptor (TCR) activation. Although stronger TCR signals lead to increased target cell death than do weaker signals, it is not known how the strength of TCR signal controls polarization of the centrosome and lytic granules. By using TCR transgenic OT-I CTLs, we showed that both high- and low-avidity interactions led to centrosome polarization to the cSMAC. However, only high-avidity interactions, which induced a higher threshold of intracellular signaling, gave rise to granule recruitment to the polarized centrosome at the synapse. By controlling centrosome and granule polarization independently, the centrosome is able to respond rapidly to weak signals so that CTLs are poised and ready for the trigger for granule delivery.