As Conversational Artificial Intelligence (AI) becomes more integrated into everyday life, AI-powered chatbot mobile applications are increasingly adopted across industries, particularly in the healthcare domain. These chatbots offer accessible and 24/7 support, yet their collection and processing of sensitive health data present critical privacy concerns. While prior research has examined chatbot security, privacy issues specific to AI healthcare chatbots have received limited attention. Our study evaluates the privacy practices of 12 widely downloaded AI healthcare chatbot apps available on the App Store and Google Play in the United States. We conducted a three-step assessment analyzing: (1) privacy settings during sign-up, (2) in-app privacy controls, and (3) the content of privacy policies. The analysis identified significant gaps in user data protection. Our findings reveal that half of the examined apps did not present a privacy policy during sign up, and only two provided an option to disable data sharing at that stage. The majority of apps' privacy policies failed to address data protection measures. Moreover, users had minimal control over their personal data. The study provides key insights for information science researchers, developers, and policymakers to improve privacy protections in AI healthcare chatbot apps.