This study is to evaluate the efficacy and safety of ARI-3037MO 3g BID compared to placebo in reducing triglyceride (TG) levels of subjects with severe (≥500 mg/dL and <2,000 mg/dL) hypertriglyceridemia. Eligible patients will enter a 4- to 6-week lead-in period (6-week washout for subjects on non-statin lipid-lowering therapy [subjects may remain on statins during this period], 4 weeks for patients on statins only or not receiving any type of lipid-lowering therapy), followed by qualifying fasting TG measurements at visits 2 and 3, at least 7 days apart. If the baseline TG value is > 500 mg/dL and < 2,000 mg/dL, the qualified subjects will be randomized at visit 4 and enter the double-blind, 12-week efficacy and safety assessment phase. End-of-study lipid levels will be assessed on visits 6 and 7 (weeks 11 and 12 average). A final closeout and safety assessment visit will be done 14 weeks post randomization