Unstable combustion was observed in a dual-chamber combustor that mimics heavy-duty gas engines utilizing prechamber jet ignition. Prechamber combustion generated a hot turbulent jet that ignited the ultra-lean H2∕air mixture in the main chamber. Thermoacoustic combustion instability was initiated for main-chamber equivalence ratio, ϕ < 0.5, and grew severe in the lean-burn regime, 0.22 < ϕ < 0.3. Simultaneous schlieren and OH chemiluminescence were used to visualize the unstable flame propagation and to characterize the instability. Classical acoustic resonator analysis and pressure spectra showed the longitudinal mode of acoustic disturbance as the primary instability mode for all equivalence ratios. However, a leaner flame was affected more due to stronger coupling between heat release and the pressure field perturbation. Transverse and mixed modes were observed at lean conditions, ϕ < 0.4. A phase-resolved measurement of strain rates along flame edge showed an oscillating strain along pressure perturbation cycle. To model the instability, 3D linearized Euler equations were solved in the frequency domain coupled with combustion response models. The physical significance of the instability modes and their behavior were identified using dynamic mode decomposition. Based on the experimental and modeling results, a mechanism for thermoacoustic instability was proposed for ultra-lean premixed H2∕air ignition by a hot turbulent jet.