This trial will establish definitive evidence on the comparative efficacy and safety of pharmacological thromboprophylaxis with the low molecular weight heparin (LMWH) enoxaparin versus no pharmacological thromboprophylaxis for the primary prevention of venous thromboembolism (VTE), including deep vein thrombosis and/or pulmonary embolism) among critically ill adolescents who meet a priori criteria for high risk of hospital-acquired (HA-) VTE. In the past two decades, the diagnosis of pediatric hospital-acquired VTE (HA-VTE) in the U.S. has increased 130-200-fold. The investigators have shown that critically-ill adolescents are one the highest risk subpopulations for HA-VTE, with average occurrence rates of 13.2% (range: 6.3-19.8%), and have derived and prospectively validated risk models for HA-VTE in this population. Despite a simultaneously increased risk of bleeding in critically ill adolescents, particularly after surgery or major trauma, an investigator-initiated multicenter phase 2 trial recently led by the investigators group during the COVID-19 pandemic demonstrated the safety of LMWH for primary HA-VTE prevention. To date, risk-stratified phase 3 Randomized Controlled Trials (RCTs) of LMWH thromboprophylaxis as primary HA-VTE prevention in children have not been performed. The investigators will perform a U.S.-based definitive multicenter phase 3 RCT of the LMWH enoxaparin versus no pharmacological thromboprophylaxis for VTE prevention among critically ill adolescents at highest a priori risk for HA-VTE applying evidence from the investigators published risk prediction models.