Contrasting Language-image pertaining (CLIP) has recently shown promising open-world and few-shot performance on 2D image-based recognition tasks. However, the transferred capability of CLIP to the novel event camera data still remains under-explored. In particular, due to the modality gap with the image-text data and the lack of large-scale datasets, achieving this goal is non-trivial and thus requires significant research innovation. In this paper, we propose E-CLIP, a novel and effective framework that unleashes the potential of CLIP for event-based recognition to compensate for the lack of large-scale event-based datasets. Our work addresses two crucial challenges: 1) how to generalize CLIP's visual encoder to event data while fully leveraging events' unique properties, e.g., sparsity and high temporal resolution; 2) how to effectively align the multi-modal embeddings, i.e., image, text, and events. To this end, we first introduce a novel event encoder that subtly models the temporal information from events and meanwhile generates event prompts to promote the modality bridging. We then design a text encoder that generates content prompts and utilizes hybrid text prompts to enhance the E-CLIP's generalization ability across diverse datasets. With the proposed event encoder, text encoder, and original image encoder, a novel Hierarchical Triple Contrastive Alignment (HTCA) module is introduced to jointly optimize the correlation and enable efficient knowledge transfer among the three modalities. We conduct extensive experiments on two recognition benchmarks, and the results demonstrate that our E-CLIP outperforms existing methods by a large margin of +3.94% and +4.62% on the N-Caltech dataset, respectively, in both fine-tuning and few-shot settings. Moreover, our E-CLIP can be flexibly extended to the event retrieval task using both text or image queries, showing plausible performance.