As artificial intelligence (AI) becomes more prevalent in our daily lives, trust has become a critical issue in ensuring that AI systems are reliable, ethical, and beneficial to society. This paper explores the role of user experience (UX) in shaping users' trust in chat AI. Chat AI has become increasingly popular as a communication tool, but users often struggle with trusting the technology. The paper examines how different design elements, such as conversational style, interface, and feedback mechanisms, affect users' perception of trust in chat AI by analyzing previous literature written in this area. Research demonstrates that UX plays a critical role in users' trust in chat AI, with factors such as transparency, responsiveness, and empathy contributing to higher levels of trust. Using the results found in the research around this topic, a redesigned prototype of a popular chat AI software called chatGPT was created with the help of Figma.