We have combined measurements of the kinematics, morphology, and oxygen abundance of the ionized gas in I Zw 18, one of the most metal-poor galaxies known, to examine the star formation history and chemical mixing processes. Deep Her imagery shows diffuse emission and a partial shell extending well beyond the two main knots of continuum emission. We have explored the kinematics of this ionized gas using long-slit echelle spectroscopy of the Hu line. We find the unambiguous signature of a supergiant shell southwest of the galaxy and weak evidence for a second bubble northeast of the galaxy. The axial symmetry of these shells and the asymmetry in their Ha line profiles suggest that they constitute the lobes of a single bipolar bubble expanding at similar to 30-60 km s(-1). Higher velocity gas is found near the small shell immediately west of the northwest H II region. Although an unresolved X-ray source is discovered near the northwest H rr region in archival ROSAT PSPC data, we argue that hot interstellar gas associated with the superbubbles does not produce all the X-ray emission, Oxygen emission lines are detected up to similar to 1 kpc from the northwest H II region along the bubble's polar axis, so this diffuse, ionized gas has been polluted with gas processed by stars. Measurements of the O/H abundance ratio in the inner nebula show surprisingly little variation, considering the apparent youth of the galaxy. We describe the dynamical evolution of the superbubble using a simple windblown-bubble model. To test the hypothesis that the dynamical age of the bubble measures the duration of the starburst in I Zw 18, we compute the photometric properties of a starburst with the same age as the superbubble. We find that star formation commencing 15-27 Myr ago and continuing at a rate of 0.017-0.021 M(.) (of 1-100 M(.) stars) per year can both power the gasdynamics and produce a fair match to the integrated optical properties of I Zw 18. The total mechanical energy returned to the interstellar medium (ISM) by stellar winds and supernovae, (7-30)x 10(53) ergs, is insufficient to eject the entire ISM. However, the corresponding mechanical energy injection rate is high enough to drive the superbubble shell out of the H I gas cloud, and ''blowout'' will allow the hot ISM to escape in a galactic wind. This supports the idea that metal-enriched winds play a prominent role in the chemical evolution of dwarf galaxies.