Sketching or doodling is a popular creative activity that people engage in. However, most existing work in automatic sketch understanding or generation has focused on sketches that are quite mundane. In this work, we introduce two datasets of creative sketches -- Creative Birds and Creative Creatures -- containing 10k sketches each along with part annotations. We propose DoodlerGAN -- a part-based Generative Adversarial Network (GAN) -- to generate unseen compositions of novel part appearances. Quantitative evaluations as well as human studies demonstrate that sketches generated by our approach are more creative and of higher quality than existing approaches. In fact, in Creative Birds, subjects prefer sketches generated by DoodlerGAN over those drawn by humans!