We present new WFPC2 narrowband imaging of the blue compact dwarf galaxy I Zw 18, which is host to the lowest metallicity H II regions known. Images at Hα and Hβ are combined with archival broadband images to allow the study of the ionized gas distribution and morphology. Analysis of the Hα/Hβ flux ratio reveals significant enhancements in some areas of both the northwest and southeast regions of the galaxy, with ratios elevated to levels as high as 3.4. The Hα/Hβ ratio varies considerably with position throughout the galaxy. Comparing this distribution with the stellar distribution indicates that the regions of enhanced Hα/Hβ ratio are not due to the effects of either collisional excitation or underlying stellar absorption and therefore are most likely interpreted as the presence of dust. This dust has an estimated mass of (2-5) × 10³ M, which is consistent with the IRAS far-IR nondetection. Under the assumption that dust traces the presence of molecular gas, these results suggest that the molecular component of the interstellar medium of I Zw 18, which is needed to fuel its active star formation, is also very clumpy. Such a distribution would be consistent with the recent Far-Ultraviolet Spectroscopic Explorer nondetections of diffuse H₂.