I think the question is interesting because I've seen a number of people making claims such as "ChatGPT cannot do this/that".
No. ChatGPT as it currently stands can execute any possible program (within practical constraints: no infinite memory/time/etc.)
Essentially, you reason that
1. If ChatGPT is turing complete, it can execute this BASIC program
2. It can execute this BASIC program
3. Therefore, it is turing complete
If you don't see the flaw in your reasoning, ask ChatGPT to explain "affirming the consequent" to you.