State-of-the-art face recognition systems are based on deep (convolutional) neural networks. Therefore, it is imperative to determine to what extent face templates derived from deep networks can be inverted to obtain the original face image. In this paper, we study the vulnerabilities of a state-of-the-art face recognition system based on template reconstruction attack. We propose a neighborly de-convolutional neural network (\textit{NbNet}) to reconstruct face images from their deep templates. In our experiments, we assumed that no knowledge about the target subject and the deep network are available. To train the \textit{NbNet} reconstruction models, we augmented two benchmark face datasets (VGG-Face and Multi-PIE) with a large collection of images synthesized using a face generator. The proposed reconstruction was evaluated using type-I (comparing the reconstructed images against the original face images used to generate the deep template) and type-II (comparing the reconstructed images against a different face image of the same subject) attacks. Given the images reconstructed from \textit{NbNets}, we show that for verification, we achieve TAR of 95.20\% (58.05\%) on LFW under type-I (type-II) attacks @ FAR of 0.1\%. Besides, 96.58\% (92.84\%) of the images reconstruction from templates of partition \textit{fa} (\textit{fb}) can be identified from partition \textit{fa} in color FERET. Our study demonstrates the need to secure deep templates in face recognition systems.