If you're talking about Martin Shkreli, the CEO of Turing Pharmaceuticals, the drug in question is Diaprim (aka Pyrimethamine). This drug has been around since the 1950s and is not, I repeat NOT subject to any sort of patent protections.
Furthermore, the drug is a treatment for toxoplasmosis not HIV. There is some confusion about this because people with weakened immune systems are especially vulnerable to the parasite which causes toxoplasmosis.
The big controversy with Diaprim arises from the fact that there are relatively few cases of this infection in the USA so there is only one manufacturer of the drug. The size of the market is so small that it's not economically viable for anyone to set up a competing operation. Therefore, Turing figures it can radically increase the price.