Machine learning models are typically made available to potential client users via inference APIs. Model extraction attacks occur when a malicious client uses information gleaned from queries to the inference API of a victim model $F_V$ to build a surrogate model $F_A$ with comparable functionality. Recent research has shown successful model extraction of image classification, and natural language processing models. In this paper, we show the first model extraction attack against real-world generative adversarial network (GAN) image translation models. We present a framework for conducting such attacks, and show that an adversary can successfully extract functional surrogate models by querying $F_V$ using data from the same domain as the training data for $F_V$. The adversary need not know $F_V$'s architecture or any other information about it beyond its intended task. We evaluate the effectiveness of our attacks using three different instances of two popular categories of image translation: (1) Selfie-to-Anime and (2) Monet-to-Photo (image style transfer), and (3) Super-Resolution (super resolution). Using standard performance metrics for GANs, we show that our attacks are effective. Furthermore, we conducted a large scale (125 participants) user study on Selfie-to-Anime and Monet-to-Photo to show that human perception of the images produced by $F_V$ and $F_A$ can be considered equivalent, within an equivalence bound of Cohen's d = 0.3. Finally, we show that existing defenses against model extraction attacks (watermarking, adversarial examples, poisoning) do not extend to image translation models.