The present-day state of stress in Tertiary deltas is poorly understood but vital for a range of applications such as wellbore stability and fracture stimulation. The Tertiary Baram Delta province, Brunei, exhibits a range of contemporary stress values that reflect the competing influence of the northwest Borneo active margin (situated underneath the basin) and local stresses generated within the delta. Vertical stress (_v) gradients at 1500-m (4921-ft) depth range from 18.3 MPa/km (0.81 psi/ft) at the shelf edge to 24.3 MPa/km (1.07 psi/ft) in the hinterland, indicating a range in the shallow bulk density across the delta of 2.07–2.48 g/cm³. The maximum horizontal stress (_Hmax) orientation rotates from margin parallel (northeast–southwest; deltaic) in the outer shelf to margin normal (northwest–southeast; basement associated) in the inner shelf. Minimum horizontal stress (_hmin) gradients in normally pressured sequences range from 13.8 to 17.0 MPa/km (0.61–0.75 psi/ft) with higher gradients observed in older parts of the basin. The variation in contemporary stress across the basin reveals a delta system that is inverting and self-cannibalizing as the delta system rapidly progrades across the margin. The present-day stress in the delta system has implications for a range of exploration and production issues affecting Brunei. Underbalanced wells are more stable if deviated toward the _hmin direction, whereas fracture stimulation in mature fields and tight reservoirs can be more easily conducted in wells deviated toward _Hmax. Finally, faults near the shelf edge are optimally oriented for reactivation, and hence exploration targets in this region are at a high risk of fault seal breach.