OpenAI's ChatGPT uses a cookie called __obi to track user behavior on other websites, allowing the company to connect user activity on those sites to their ChatGPT account. This tracking mechanism is similar to those used by other companies like Facebook and Google. The cookie is set when a user visits ChatGPT and is sent to OpenAI when the user visits other websites that have installed OpenAI's ad code. The tracking is used for advertising purposes, but some users may be unaware of the extent of the tracking.