We present the Chandra imaging and spectral analysis of NGC 4968, a nearby (z = 0.00986) Seyfert 2 galaxy. We discover extended (∼1 kpc) X-ray emission in the soft band (0.5 - 2 keV) that is neither coincident with the narrow line region nor the extended radio emission. Based on spectral modeling, it is linked to on-going star formation (∼2.6-4 M_ yr^-1). The soft emission at circumnuclear scales (inner ∼400 pc) originates from hot gas, with kT ∼ 0.7 keV, while the most extended thermal

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... is cooler (kT ∼ 0.3 keV). We refine previous measurements of the extreme Fe Kα equivalent width in this source (EW = 2.5^+2.6_-1.0 keV), which suggests the central engine is completely embedded within Compton-thick levels of obscuration. Using physically motivated models fit to the Chandra spectrum, we derive a Compton-thick column density (N_ H > 1.25×10^24 cm^-2) and an intrinsic hard (2-10 keV) X-ray luminosity of ∼3-8× 10^42 erg s^-1 (depending on the presumed geometry of the obscurer), which is over two orders of magnitude larger than that observed. The large Fe Kα EW suggests a spherical covering geometry, which could be confirmed with X-ray measurements above 10 keV. NGC 4968 is similar to other active galaxies that exhibit extreme Fe Kα EWs (i.e., >2 keV) in that they also contain ongoing star formation. This work supports the idea that gas associated with nuclear star formation may increase the covering factor of the enshrouding gas and play a role in obscuring AGN.