Some GPs in some EU countries did decide do take it prophylactically due to lack of PPE. But most around me agree this is a risky and probably bad advice. The current publicly available guidelines do not recommend taking it before you develop symptoms and do not recommend taking it at all if you are asymptomatic and/or very young. And also certainly they do not recommend any self medication without doctor's approval as there can be serious adverse effects with chloroquine (less with hydroxichloroquine).

Also this would have a terrible effect and indeed cause supply shortages as another commenter pointed out.