I have been through this several times in startups and in operating companies.
I have read the responses to date and tried the lenient methods to my regret.
Dismiss him ASAP. The bad attitude will permeate your company for many years.
Eventually it will contaminate all your employees and exhaust you.
In my experience the longer you allow him to remain the greater the damage. In retrospect I would have been much better closing several of the startups rather than spend years trying to root out the bad attitudes.
In the operating company the tech was immediately dismissed and other employees noted that insubordination, back stabbing and playing politics was not tolerated.
The start up died with several million dollars in debt. The operating company is still going and stronger than ever.
PS dismissing is especially important if you are not the technical person.