We introduce CLOB, a novel continual learning (CL) paradigm wherein a large language model (LLM) is regarded as a black box. Learning is done incrementally via only verbal prompting. CLOB does not fine-tune any part of the LLM or add any trainable parameters to it. It is particularly suitable for LLMs that are accessible via APIs. We also propose a new CL technique, called CIS, based on incremental summarization that also overcomes the LLM's input length limit. Experiments show CIS outperforms baselines by a very large margin.