REST APIs (Representational State Transfer Application Programming Interfaces) are an indispensable building block in today's cloud-native applications, so testing them is critically important. However, writing automated tests for such REST APIs is challenging because one needs strong and readable tests that exercise the boundary values of the protocol embedded in the REST API. In this paper, we report our experience with using "out of the box" large language models (ChatGPT and GitHub's Copilot) to amplify REST API test suites. We compare the resulting tests based on coverage and understandability, and we derive a series of guidelines and lessons learned concerning the prompts that result in the strongest test suite.