The local structure of CeTe3 in the incommensurate charge density wave (IC-CDW) state has been obtained using atomic pair distribution function (PDF) analysis of x-ray diffraction data. Local atomic distortions in the Te-nets due to the CDW are larger than observed crystallographically, resulting in distinct short and long Te-Te bonds. Observation of different distortion amplitudes in the local and average structures are explained by the discommensurated nature of the CDW since the PDF is sensitive to the local displacements within the commensurate regions whereas the crystallographic result averages over many discommensurated domains. The result is supported by STM data. This is the first quantitative local structural study within the commensurate domains in an IC-CDW system.