Large Language Models (LLMs) are vulnerable to `Jailbreaking' prompts, a type of attack that can coax these models into generating harmful and illegal content. In this paper, we show that pruning up to 20% of LLM parameters markedly increases their resistance to such attacks without additional training and without sacrificing their performance in standard benchmarks. Intriguingly, we discovered that the enhanced safety observed post-pruning correlates to the initial safety training level of the model, hinting that the effect of pruning could be more general and may hold for other LLM behaviors beyond safety. Additionally, we introduce a curated dataset of 225 harmful tasks across five categories, inserted into ten different Jailbreaking prompts, showing that pruning aids LLMs in concentrating attention on task-relevant tokens in jailbreaking prompts. Lastly, our experiments reveal that the prominent chat models, such as LLaMA-2 Chat, Vicuna, and Mistral Instruct exhibit high susceptibility to jailbreaking attacks, with some categories achieving nearly 70-100% success rate. These insights underline the potential of pruning as a generalizable approach for improving LLM safety, reliability, and potentially other desired behaviors.