How many times can a human get chicken pox?
Usually you get chicken pox only once in your life, the recurring form are usually shingles.  But: It can happen (also in people which are not immunocompromized). I know two persons which got chicken pox twice and which are otherwise normal in regards of their immune system.

Persons with an HIV infection are more at risk here. They can develop both forms and depending on how much their immune system is already affected by the HIV infection can develop severe forms of the infection. It might be necessary to treat them with antiviral drugs. So it is clearly recommended to ask a MD about this. See here for more details.