In ventricular fibrillation (VF), the principal cause of sudden cardiac death, waves of electrical excitation break up into turbulent and incoherent fragments. The causes of this breakup have been intensely debated. Breakup can be caused by fixed anatomical properties of the tissue, such as the biventricular geometry and the inherent anisotropy of cardiac conduction. However, wavebreak can also be caused purely by instabilities in wave conduction that arise from ion channel dynamics, which represent potential targets for drug action. To study the interaction between these two wave-breaking mechanisms, we used a physiologically based mathematical model of the ventricular cell, together with a realistic three-dimensional computer model of cardiac anatomy, including the distribution of fiber angles throughout the myocardium. We find that dynamical instabilities remain a major cause of the wavebreak that drives VF, even in an anatomically realistic heart. With cell physiology in its usual operating regime, dynamics and anatomical features interact to promote wavebreak and VF. However, if dynamical instability is reduced, for example by modeling of certain pharmacologic interventions, electrical waves do not break up into fibrillation, despite anatomical complexity. Thus, interventions that promote dynamical wave stability show promise as an antifibrillatory strategy in this more realistic setting.