RSA and AES do not oppose, and often are rightly used together in [hybrid encryption](https://en.wikipedia.org/wiki/Hybrid_cryptosystem). RSA can do things that AES can not, like allowing encryption to designated recipients, or allowing anyone to check that a message is not altered or from a different person than is apparent. Using AES or other form of symmetric encryption is a must when encrypting more than few hundred characters.

To choose a cryptosystem, you must first define your goals. _Secure chat_ is not nearly precise enough. Confidentiality? Integrity? Proof of origin? Central registry of participants? How is registration and loss of keys handled?