In this paper, we study the vulnerability of large-scale language models (LLMs) to hardware-based threats, especially bit-flip attacks (BFA). While previous works claim that transformer-based architectures are more robust against BFA, we show that even a few bit-flips can severely degrade the performance of LLMs with billions of parameters. To address this issue, we propose AttentionBreaker, a novel framework that efficiently explores the parameter space of LLMs to identify important parameters, and GenBFA, an evolutionary optimization strategy that finds the most significant bits. Experimental results demonstrate that AttentionBreaker exposes a serious vulnerability of LLMs, where even a few bit-flips can completely collapse the model performance.