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We present the physical extent of [CII] 158um line-emitting gas from 46 star-forming galaxies at z=4-6 from the ALMA Large Program to INvestigate CII at Early Times (ALPINE). Using exponential profile fits, we measure the effective radius of the [CII] line (r_e,[CII]) for individual galaxies and compare them with the rest-frame ultra-violet (UV) continuum (r_e,UV) from Hubble Space Telescope images. The effective radius r_e,[CII] exceeds r_e,UV by factors of ~2-3 and the ratio of r_e,[CII]/r_e,UV increases as a function of M_star. We do not find strong evidence that [CII] line, the rest-frame UV, and FIR continuum are always displaced over ~ 1-kpc scale from each other. We identify 30% of isolated ALPINE sources as having an extended [CII] component over 10-kpc scales detected at 4.1$σ$-10.9$σ$ beyond the size of rest-frame UV and far-infrared (FIR) continuum. One object has tentative rotating features up to ~10-kpc, where the 3D model fit shows the rotating [CII]-gas disk spread over 4 times larger than the rest-frame UV-emitting region. Galaxies with the extended [CII] line structure have high star-formation rate (SFR), stellar mass (M_star), low Lya equivalent-width, and more blue-shifted (red-shifted) rest-frame UV metal absorption (Lya line), as compared to galaxies without such extended [CII] structures. Although we cannot rule out the possibility that a selection bias towards luminous objects may be responsible for such trends, the star-formation driven outflow also explains all these trends. Deeper observations are essential to test whether the extended [CII] line structures are ubiquitous to high-z star-forming galaxies.