We introduce the Single Stage Headless (SSH) face detector. Unlike two stage proposal-classification detectors, SSH detects faces in a single stage directly from the early convolutional layers in a classification network. SSH is headless. That is, it is able to achieve state-of-the-art results while removing the "head" of its underlying classification network -- i.e. all fully connected layers in the VGG-16 which contains a large number of parameters. Additionally, instead of relying on an image pyramid to detect faces with various scales, SSH is scale-invariant by design. We simultaneously detect faces with different scales in a single forward pass of the network, but from different layers. These properties make SSH fast and light-weight. Surprisingly, with a headless VGG-16, SSH beats the ResNet-101-based state-of-the-art on the WIDER dataset. Even though, unlike the current state-of-the-art, SSH does not use an image pyramid and is 5X faster. Moreover, if an image pyramid is deployed, our light-weight network achieves state-of-the-art on all subsets of the WIDER dataset, improving the AP by 2.5%. SSH also reaches state-of-the-art results on the FDDB and Pascal-Faces datasets while using a small input size, leading to a runtime of 50 ms/image on a GPU. The code is available at https://github.com/mahyarnajibi/SSH.