We use the three-dimensional (3D) stellar structure code DJEHUTY to model the ingestion of protons into the intershell convection zone of a 1 M(circle dot) asymptotic giant branch star of metallicity Z = 10(-4). We have run two simulations: a low-resolution one of around 300,000 zones and a high-resolution one consisting of 2,000,000 zones. Both simulations have been evolved for about 4 hr of stellar time. We observe the existence of fast, downward flowing plumes that are able to transport hydrogen into close proximity to the helium-burning shell before burning takes place. The intershell in the 3D model is richer in protons than the 1D model by several orders of magnitude and so we obtain substantially higher hydrogen-burning luminosities-over 10(8) L(circle dot) in the high-resolution simulation-than are found in the 1D model. Convective velocities in these simulations are over ten times greater than the predictions of mixing length theory, though the 3D simulations have greater energy generation due to the enhanced hydrogen burning. We find no evidence of the convective zone splitting into two, though this could be as a result of insufficient spatial resolution or because the models have not been evolved for long enough. We suggest that the 1D mixing length theory and particularly the use of a diffusion algorithm for mixing do not give an accurate picture of these events. An advective mixing scheme may give a better representation of the transport processes seen in the 3D models.