This paper presents a new side channel that affects mixed-signal chips used in widespread wireless communication protocols, such as Bluetooth and WiFi. This increasingly common type of chip includes the radio transceiver along with digital logic on the same integrated circuit. In such systems, the radio transmitter may unintentionally broadcast sensitive information from hardware cryptographic components or software executing on the CPU. The well-known electromagnetic (EM) leakage from digital logic is inadvertently mixed with the radio carrier, which is amplified and then transmitted by the antenna. We call the resulting leak “screaming channels”. Attacks exploiting such a side channel may succeed over a much longer distance than attacks exploiting usual EM side channels. The root of the problem is that mixed-signal chips include both digital circuits and analog circuits on the same silicon die in close physical proximity. While processing data, the digital circuits on these chips generate noise, which can be picked up by noise-sensitive analog radio components, ultimately leading to leakage of sensitive information. We investigate the physical reasons behind the channel, we measure it on several popular devices from different vendors (including Nordic Semiconductor nRF52832, and Qualcomm Atheros AR9271), and we demonstrate a complete key recovery attack against the nRF52832 chip. In particular, we retrieve the full key from the AES-128 implementation in tinyAES at a distance of 10 m using template attacks. Additionally, we recover the key used by the AES-128 implementation in mbedTLS at a distance of 1 m with a correlation attack. Screaming channel attacks change the threat models of devices with mixed-signal chips, as those devices are now vulnerable from a distance. More specifically, we argue that protections against side channels (such as masking or hiding) need to be used on this class of devices. Finally, chips implementing other widespread protocols (e.g., 4G/LTE, RFID) need to be inspected to determine whether they are vulnerable to screaming channel attacks.