Existing face hallucination methods based on convolutional neural networks (CNNs) 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 non-uniform illumination conditions. This paper proposes a Recursive Copy and Paste Generative Adversarial Network (Re-CPGAN) to recover authentic high-resolution (HR) face images while compensating for non-uniform illumination. To this end, we develop two key components in our Re-CPGAN: internal and recursive external Copy and Paste networks (CPnets). Our internal CPnet exploits facial self-similarity information residing in the input image to enhance facial details; while our recursive external CPnet leverages an external guided face for illumination compensation. Specifically, our recursive external CPnet stacks multiple external Copy and Paste (EX-CP) units in a compact model to learn normal illumination and enhance facial details recursively. By doing so, our method offsets illumination and upsamples facial details progressively in a coarse-to-fine fashion, thus alleviating the ambiguity of correspondences between LR inputs and external guided inputs. Furthermore, a new illumination compensation loss is developed to capture illumination from the external guided face image effectively. Extensive experiments demonstrate that our method achieves authentic HR face images in a uniform illumination condition with a $16\times$ magnification factor and outperforms state-of-the-art methods qualitatively and quantitatively.