Existing face hallucination methods based on convolutional neural networks (CNN) have achieved impressive performance on low-resolution (LR) faces in a normal illumination condition. However, their performance degrades dramatically when LR faces are captured in low or non-uniform illumination conditions. This paper proposes a Copy and Paste Generative Adversarial Network (CPGAN) to recover authentic high-resolution (HR) face images while compensating for low and non-uniform illumination. To this end, we develop two key components in our CPGAN: internal and external Copy and Paste nets (CPnets). Specifically, our internal CPnet exploits facial information residing in the input image to enhance facial details; while our external CPnet leverages an external HR face for illumination compensation. A new illumination compensation loss is thus developed to capture illumination from the external guided face image effectively. Furthermore, our method offsets illumination and upsamples facial details alternately in a coarse-to-fine fashion, thus alleviating the correspondence ambiguity between LR inputs and external HR inputs. Extensive experiments demonstrate that our method manifests authentic HR face images in a uniform illumination condition and outperforms state-of-the-art methods qualitatively and quantitatively.