P300 speller BCIs allow users to compose sentences by selecting target keys on a GUI through the detection of P300 component in their EEG signals following visual stimuli. Most P300 speller BCIs require users to spell words letter by letter, or the first few initial letters, resulting in high keystroke demands that increase time, cognitive load, and fatigue. This highlights the need for more efficient, user-friendly methods for faster sentence composition. In this work, we introduce ChatBCI, a P300 speller BCI that leverages the zero-shot learning capabilities of large language models (LLMs) to suggest words from user-spelled initial letters or predict the subsequent word(s), reducing keystrokes and accelerating sentence composition. ChatBCI retrieves word suggestions through remote queries to the GPT-3.5 API. A new GUI, displaying GPT-3.5 word suggestions as extra keys is designed. SWLDA is used for the P300 classification. Seven subjects completed two online spelling tasks: 1) copy-spelling a self-composed sentence using ChatBCI, and 2) improvising a sentence using ChatBCI's word suggestions. Results demonstrate that in Task 1, on average, ChatBCI outperforms letter-by-letter BCI spellers, reducing time and keystrokes by 62.14% and 53.22%, respectively, and increasing information transfer rate by 198.96%. In Task 2, ChatBCI achieves 80.68% keystroke savings and a record 8.53 characters/min for typing speed. Overall, ChatBCI, by employing remote LLM queries, enhances sentence composition in realistic scenarios, significantly outperforming traditional spellers without requiring local model training or storage. ChatBCI's (multi-) word predictions, combined with its new GUI, pave the way for developing next-generation speller BCIs that are efficient and effective for real-time communication, especially for users with communication and motor disabilities.