Closed-loop brain-implantable neuromodulation devices are a new treatment option for patients with refractory epilepsy. Seizure detection algorithms implemented on such devices are subject to strict power and area constraints. Deep learning methods, though very powerful, tend to have high computational complexity and thus are typically impractical for resource-constrained neuromodulation devices. In this paper, we propose a compact and hardware-efficient one-dimensional convolutional neural network (1D CNN) structure for patient-specific early seizure detection. Feature extraction techniques and a novel initialization method based on the forward-chaining training and testing scheme are used to improve model performance. Our compact model achieves similar accuracy to that of support vector machines, the state-of-the-art method for seizure detection, while consuming over 20x less power.