Large language models (LLMs) find increasing applications in many fields. Here, three LLM chatbots (ChatGPT-3.5, ChatGPT-4, and Bard) are assessed in their current form, as publicly available, for their ability to recognize Alzheimer’s dementia (AD) and Cognitively Normal (CN) individuals using textual input derived from spontaneous speech recordings. A zero-shot learning approach is used at two levels of independent queries, with the second query (chain-of-thought prompting) eliciting more detailed information than the first. Each LLM chatbot’s performance is evaluated on the prediction generated in terms of accuracy, sensitivity, specificity, precision, and F1 score. LLM chatbots generated a three-class outcome (“AD”, “CN”, or “Unsure”). When positively identifying AD, Bard produced the highest true-positives (89% recall) and highest F1 score (71%), but tended to misidentify CN as AD, with high confidence (low “Unsure” rates); for positively identifying CN, GPT-4 resulted in the highest true-negatives at 56% and highest F1 score (62%), adopting a diplomatic stance (moderate “Unsure” rates). Overall, the three LLM chatbots can identify AD vs. CN, surpassing chance-levels, but do not currently satisfy the requirements for clinical application.