This research will study the effects of early initiation of alirocumab in addition to high intensity statin therapy in patients who have previously been treated with high intensity statins with poor response, who present with a type I (spontaneous) acute NSTEMI. Patients will be dosed with drug or placebo once during the first day of their hospital admission. Blood samples will be collected at baseline, 3 days and 14 days after randomization for biomarker testing. Particular attention will be paid to additional LDL lowering effects, as well as the effects on PCSK9 levels and inflammatory biomarkers. Safety and tolerability will be monitored with complete blood count + differential and complete metabolic panels at each study visit.