A Phase 1b study for subjects with Stage IIIB/IV NSCLC to participate in 1 of 2 portions of this study. The first portion is Dose Escalation in which subjects are tested with PEGPH20 at various doses (1.6, 3.0, 2.2 and 2.8 mcg/kg) in addition to dosing with the standard dose of docetaxel of 75 mg/m2 (PDoc) once every 21-day cycle. 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 will be tested, 2.2 and 2.8 mcg/kg. Up to 30 additional subjects may be enrolled to test these dose levels. The second portion of Phase 1b is Cohort Expansion in which the recommended Phase 2 dose (RP2D) of PDoc identified in dose escalation is administered every 21 days to approximately 50 subjects with high hyaluronan (HA-high) prospectively measured in their tumor tissue.