A widespread view is that Artificial Intelligence cannot be creative. We tested this assumption by comparing human-generated ideas with those generated by six Generative Artificial Intelligence (GAI) chatbots: $alpa.\!ai$, $Copy.\!ai$, ChatGPT (versions 3 and 4), $Studio.\!ai$, and YouChat. Humans and a specifically trained AI independently assessed the quality and quantity of ideas. We found no qualitative difference between AI and human-generated creativity, although there are differences in how ideas are generated. Interestingly, 9.4 percent of humans were more creative than the most creative GAI, GPT-4. Our findings suggest that GAIs are valuable assistants in the creative process. Continued research and development of GAI in creative tasks is crucial to fully understand this technology's potential benefits and drawbacks in shaping the future of creativity. Finally, we discuss the question of whether GAIs are capable of being truly creative.