STUDY DESIGN: We propose a randomized double-blind placebo-controlled pilot study of prophylactic LMWH in women at moderate to high risk for VTE following cesarean section. Eligible, consenting and randomized participants will receive once-daily injections of study drug (4,500 IU tinzaparin sodium (Innohep®;) or placebo) within 6 to 24 hours postpartum and continue until 3 to 7 days postpartum. On the day of hospital discharge, bilateral leg imaging with compression leg ultrasounds and pelvic vein imaging with MRV will be completed. The primary outcome will be adjudicated DVT documented on ultrasounds or MRV on the day of hospital discharge. Secondary outcomes will include symptomatic DVT and PE, death from PE, major and minor bleeding, HIT during the six week postpartum period. All outcomes will be adjudicated by an independent committee of experts blinded to study drug allocation.