Hubble archival images of NGC 6543 reveal a series of at least nine regularly spaced concentric circular rings that surround the famous nebular core, known as the Cat's Eye Nebula. The rings are almost certainly spherical bubbles of periodic isotropic nuclear mass pulsations that preceded the formation of the core. The bubbles are detected solely in the lines of H alpha, [O III], and [N II]. The core and the bubbles around it appear to have very similar temperature, ionization, and chemical properties. Assuming a distance of 1 kpc and an outflow velocity of 10 km s(-1), a good fit to the Ha surface brightness distribution suggests that the bubbles were ejected with constant mass (similar to 0.01 M-.) and thickness (similar to 1000 AU) approximately every 1500 years. The combined mass of the visible bubbles, similar to0.1 M-., is comparable to that of the present mass of the core (similar to0.05 M-.). Since the bubbles are evenly spaced and there is no sign of bubble-bubble collisions, the bubble ejection mechanism regulates the outflow speed to better than 10%. The line widths of the bubbles, similar to 30 km s(-1), argue that the bubbles are in the process of thickening and merging on timescales less than or similar to 10(3) yr. Their ejection period is consistent with a suggestion that quasi-periodic shells are launched every few hundred years in dust-forming asymptotic giant branch (AGB) winds but not consonant with the predictions of extant models of core thermal pulses (similar to 105 yr) and surface pulsations (similar to 10 yr). It appears that regular isotropic AGB mass pulses can precede the formation of brighter, denser, and more complex planetary nebula cores that are formed when an abrupt change of mode of mass loss occurs. Disruptive binary companion mergers or the sudden emergence of a magnetic field might account for the mode change.