Long-Term Evolution (LTE) communication is based on an open medium; thus, a legitimate signal can potentially be counterfeited by a malicious signal. Although most LTE signaling messages are protected from modification using cryptographic primitives, broadcast messages in LTE have never been integrity protected. In this paper, for the first time, we present a signal injection attack that exploits the fundamental weaknesses of broadcast messages in LTE and modifies a transmitted signal over the air. This attack, which is referred to as signal overshadowing (named SigOver) has several advantages and differences when compared with existing attacks using a fake base station. For example, with a 3 dB power difference from a legitimate signal, the SigOver attack demonstrated a 98% success rate when compared with the 80% success rate of attacks achieved using a fake base station, even with a 35 dB power difference. Given that the SigOver attack is a novel primitive attack, it yields five new attack scenarios and implications. Finally, a discussion on two potential countermeasures leaves practical and robust defense mechanism as a future work.