Firstly HIV is a virus. Viruses do not stain gram positive or negative to a gram stain. Plus they are way too small to be seen under a normal microscope. Its bacteria that stain negative or positive to a gram stain with a very few exceptions and no HIV is a virus not a bacteria. HIV= Human immunodeficiency virus
A Gram-negative bacteria is the one that does not retain crystal violet dye in the Gram staining protocol whereas a Gram-positive bacteria is the one that retains a crystal violet dye during the Gram stain process. HIV Virus can be caused by both these bacteria.