Criteria to identify potential candidates for study inclusion will include: 1) Critically ill adult patients ≥ 16 years of age admitted to an adult ICU for any reason with suspected, probable or confirmed novel swine origin influenza A/H1N1 infection (see Additional File 1). 2) Requiring mechanical ventilation (invasive or noninvasive) 3) Receiving antiviral therapy (any medication at any dose and for any intended duration) for ≤ 72 hours 4) Attending physician or intensivist must have a 'moderate' to 'high' index of suspicion for H1N1. 3) Weight < 40 kg 4) Unable to receive or unlikely to absorb enteral study drug (e.g., incomplete or complete bowel obstruction, intestinal ischemia, infarction, short bowel syndrome) 5) Rosuvastatin specific exclusions: a. Already receiving a statin b. Allergy or intolerance to statins. c. Receiving niacin, fenofibrate, cyclosporine, gemfibrozil, any protease inhibitor (including but not limited to lopinavir and ritonavir) or planned use of oral contraceptives or estrogen therapy during the ICU stay. d. CK exceeds 5,000 U/L or ALT exceeds 8 times the upper limit of normal (ULN). 6) Severe chronic liver disease (Child-Pugh Score 11-15) (see Additional File 2) 7) Previous enrolment in this trial 8) Pregnancy or breast feeding 9) At the time of enrolment, receipt of > 72 hours of antiviral therapy. 10) Known or suspected clinically significant myositis or myopathy.