Kill Or Be Killed #1 by Ed Brubaker

A depressed grad student in New York survives a suicide attempt and is visited by a sinister entity that claims his life was spared on the condition that he kill one person each month. Torn between disbelief and fear, he begins to rationalize vigilante justice, targeting those he deems predatory, even as his tangled relationships and fragile mental state push him deeper into a moral and psychological spiral.