The recent Chandra discovery of extended $sim$kpc-scale hard ($>$ 3 keV) X-ray emission in nearby Compton-thick (CT) active galactic nuclei (AGN) opens a new window to improving AGN torus modeling and investigating how the central super massive black hole interacts with and impacts the host galaxy. Since there are only a handful of detections so far, we need to establish a statistical sample to determine the ubiquity of the extended hard X-ray emission in CT AGN, and quantify the amount and extent of this component. In this paper, we present the spatial analysis results of a pilot Chandra imaging survey of 7 nearby ($0.006 < z < 0.013$) CT AGN selected from the Swift-BAT spectroscopic AGN survey. We find that five out of the seven CT AGN show extended emission in the 3-7 keV band detected at $>$ 3$sigma$ above the Chandra PSF with $sim$12% to 22% of the total emission in the extended components. ESO 137-G034 and NGC 3281 display biconical ionization structures with extended hard X-ray emission reaching kpc-scales ($sim$ 1.9 kpc and 3.5 kpc in diameter). The other three show extended hard X-ray emission above the PSF out to at least $sim$360 pc in radius. We find a trend that a minimum 3-7 keV count rate of 0.01 cts/s and total excess fraction $>$20% is required to detect a prominent extended hard X-ray component. Given that this extended hard X-ray component appears to be relatively common in this uniformly selected CT AGN sample, we further discuss the implications for torus modeling and AGN feedback.
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