The use of chatbots equipped with artificial intelligence (AI) in educational settings has increased in recent years, showing potential to support teaching and learning. However, the adoption of these technologies has raised concerns about their impact on academic integrity, students' ability to problem-solve independently, and potential underlying biases. To better understand students' perspectives and experiences with these tools, a survey was conducted at a large public university in the United States. Through thematic analysis, 262 undergraduate students' responses regarding their perceived benefits and risks of AI chatbots in education were identified and categorized into themes. The results discuss several benefits identified by the students, with feedback and study support, instruction capabilities, and access to information being the most cited. Their primary concerns included risks to academic integrity, accuracy of information, loss of critical thinking skills, the potential development of overreliance, and ethical considerations such as data privacy, system bias, environmental impact, and preservation of human elements in education. While student perceptions align with previously discussed benefits and risks of AI in education, they show heightened concerns about distinguishing between human and AI generated work - particularly in cases where authentic work is flagged as AI-generated. To address students' concerns, institutions can establish clear policies regarding AI use and develop curriculum around AI literacy. With these in place, practitioners can effectively develop and implement educational systems that leverage AI's potential in areas such as immediate feedback and personalized learning support. This approach can enhance the quality of students' educational experiences while preserving the integrity of the learning process with AI.