This is a Phase 1b study for subjects with Stage IIIB/IV NSCLC to participate in 1 of 2 portions of this study. The first portion of the Phase 1b is Dose Escalation which will enroll up to 30 subjects testing various dose levels of PEGPH20 (1.6, 2.2, 2.8 and 3.0 mcg/kg) plus docetaxel 75mg/m2 once every 3 weeks until the maximum tolerated dose or MTD is found. Based on observations on the safety and tolerability of study treatment from dose escalation cohorts dosed to date (1.6 and 3.0 mcg/kg of PEGPH20), two additional dose levels, 2.2 and 2.8 mcg/kg will be tested. The 2nd portion of Phase 1b is Cohort Expansion. This portion will enroll approximately 50 subjects at the MTD/RP2D of PDoc given every 21-day cycle. These subjects will be pre-selected with high levels of HA measured in their tumor tissue sample prior to enrollment. After the Phase 1b is completed, all data will be analyzed and the safest, best tolerated and most efficacious dose of PDoc will be used in a planned separate Phase 2 study.