The recent Chandra discovery of extended ∼kiloparsec-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 supermassive 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 seven nearby ( $0.006\lt z\lt 0.013$ ) 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 >3σ above the Chandra point-spread function (PSF), with ∼12%-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 kiloparsec scales (∼1.9 and 3.5 kpc in diameter). The other three show extended hard X-ray emission above the PSF out to at least ∼360 pc in radius. We find a trend that a minimum 3-7 keV count rate of 0.01 counts s-1 and total excess fraction >20% are 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.