No. Refusing to hire someone or firing them because they are HIV-positive is illegal. The only narrow exception is if:

• A qualified and independent doctor provides a written certificate stating that you pose a significant risk of HIV transmission at your workplace or that you are unfit to perform your job duties, AND 
• Your employer provides a written statement explaining why they cannot make reasonable adjustments to accommodate you due to administrative or financial difficulties. 

If these conditions are not met, it is legally presumed that you are fit to perform your job.