A developer built a real-time chat application using Twilio Chat and lit-html, a templating library for web applications. The chat application allows users to send messages in real-time and updates the UI efficiently using lit-html's browser-native functionality. The application uses code-splitting with Parcel to improve page load time by only loading necessary code on initial page load. The developer also generated an access token dynamically using Twilio Functions, a serverless function service, to authenticate users before starting the chat session.