ChatTTS is a high-quality open-source text-to-speech library that can be integrated into applications. To run ChatTTS using Modal, a serverless cloud computing platform, developers need to create an account at modal.com, install the Modal Python package, and authenticate their account. They then set up the environment by importing required libraries, configuring an image with necessary dependencies, creating a TTS class that handles text-to-speech conversion, and defining a local entrypoint to run the conversion. The script can be saved in a file named chattts_modal.py and run using Modal, generating an output.wav file with synthesized speech.