We present bidimensional, long-slit spectroscopic mapping of the prototypical low-metallicity dwarf galaxy I Zw 18. A total of eight spaced slit positions were observed, covering most of the body of the galaxy and part of the extended envelope of the diffuse ionized halo seen in deep Hα images of I Zw 18. Spectroscopic maps of the galaxy have been produced for Hα, Hβ equivalent width, [O III], [O II], reddening, excitation, and line-free continuum. Chemical abundances have been derived for 16 positions in I Zw 18, including zones sampling part of the extended ionized envelope of the galaxy. Our results confirm and extend previous findings that I Zw 18 presents a substantially homogeneous chemical composition over the whole galaxy. The chemical abundances of I Zw 18 as derived from a sigma-weighted average of all the observed positions give 12 + log O/H = 7.19 +/- 0.07 and 12 + log N/H = 5.64 +/- 0.12 for oxygen and nitrogen, respectively, and He/H = 0.073 +/- 0.004 for helium, a value consistent with some previous determinations and one that would lead to a helium mass fraction of Y = 0.228 +/- 0.009. However, we notice that when the bright central knots are excluded from the mean, a slightly larger helium abundance is derived, yielding Y = 0.242 +/- 0.010. We argue that underlying stellar absorption in the helium lines is present in the spectra of the central bright knots of I Zw 18 and will be affecting the derivation of the helium abundance for these central knots. The implications of our results for the chemical evolution models and for the overall enrichment history of the I Zw 18 galaxy are discussed.