How perplexing does "I don't think I might get the job" sound to your ears?

I don't think I might get the job

According to ChatGPT, it is ungrammatical because it is no longer a prediction but a denial and a situation assessment rather than a mere prediction, though I think it's still a prediction, if a very strong one, certainly stronger than one with will, but simply many native English speakers prefer to negate the modal rather than using the don't construction since they deem it unnecessary.

Am I right?

I don't know about 'ungrammatical', but it's certainly very unidiomatic. There are many more natural ways to express the idea.

I don't think I'm likely to get the job.

I probably won't get the job.

I don't have much chance of getting the job.