We present 0.15-arcsec (1 kpc) resolution ALMA observations of the [CII] 157.74 um line and rest-frame 160-um continuum emission in two z~3 dusty, star-forming galaxies - ALESS 49.1 and ALESS 57.1, combined with resolved CO(3-2) observations. In both sources, the [CII] surface brightness distribution is dominated by a compact core $leq$1 kpc in radius, a factor of 2-3 smaller than the extent of the CO(3-2) emission. In ALESS 49.1, we find an additional extended (8-kpc radius), low surface-brightness [CII] component. Based on an analysis of mock ALMA observations, the [CII] and 160-um continuum surface brightness distributions are inconsistent with a single-Gaussian surface brightness distribution with the same size as the CO(3-2) emission. The [CII] rotation curves flatten at $simeq$2 kpc radius, suggesting the kinematics of the central regions are dominated by a baryonic disc. Both galaxies exhibit a strong [CII]/FIR deficit on 1-kpc scales, with FIR-surface-brightness to [CII]/FIR slope steeper than in local star-forming galaxies. A comparison of the [CII]/CO(3-2) observations with PDR models suggests a strong FUV radiation field ($G_0sim10^4$) and high gas density ($nmathrm{(H)}sim10^4-10^5$ cm$^{-3}$) in the central regions of ALESS 49.1 and 57.1. The most direct interpretation of the pronounced [CII]/FIR deficit is a thermal saturation of the C+ fine-structure levels at temperatures $geq$500 K, driven by the strong FUV field.
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