To prevent tracking, the Bluetooth Low Energy protocol integrates privacy mechanisms such as address randomization. However, as highlighted by previous researches address randomization is not a silver bullet and can be circumvented by exploiting other types of information disclosed by the protocol such as counters or timing. In this work, we propose a novel attack to break address randomization in BLE exploiting side information that has not been considered before: Received Signal Strength Indication (RSSI). More precisely, we demonstrate how RSSI measurements, extracted from received BLE advertising packets, can be used to link together the traces emitted by the same device or re-identify it despite address randomization. The proposed attack leverages the distribution of RSSI to create a fingerprint of devices. An empirical evaluation of the attack on various scenarios demonstrate its effectiveness. For instance in the static context, in which devices remain at the same position, the proposed approach yields a re-identification accuracy of up to 99%, which can even be boosted by increasing the number of receivers controlled by the adversary.