Loneliness and social isolation are serious and widespread problems among older people, affecting their physical and mental health, quality of life, and longevity. In this paper, we propose a ChatGPT-based conversational companion system for elderly people. The system is designed to provide companionship and help reduce feelings of loneliness and social isolation. The system was evaluated with a preliminary study. The results showed that the system was able to generate responses that were relevant to the created elderly personas. However, it is essential to acknowledge the limitations of ChatGPT, such as potential biases and misinformation, and to consider the ethical implications of using AI-based companionship for the elderly, including privacy concerns.