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In this paper, we present a low-power anomaly detection integrated circuit (ADIC) based on a one-class classifier (OCC) neural network. The ADIC achieves low-power operation through a combination of (a) careful choice of algorithm for online learning and (b) approximate computing techniques to lower average energy. In particular, online pseudoinverse update method (OPIUM) is used to train a randomized neural network for quick and resource efficient learning. An additional 42% energy saving can be achieved when a lighter version of OPIUM method is used for training with the same number of data samples lead to no significant compromise on the quality of inference. Instead of a single classifier with large number of neurons, an ensemble of K base learner approach is chosen to reduce learning memory by a factor of K. This also enables approximate computing by dynamically varying the neural network size based on anomaly detection. Fabricated in 65nm CMOS, the ADIC has K = 7 Base Learners (BL) with 32 neurons in each BL and dissipates 11.87pJ/OP and 3.35pJ/OP during learning and inference respectively at Vdd = 0.75V when all 7 BLs are enabled. Further, evaluated on the NASA bearing dataset, approximately 80% of the chip can be shut down for 99% of the lifetime leading to an energy efficiency of 0.48pJ/OP, an 18.5 times reduction over full-precision computing running at Vdd = 1.2V throughout the lifetime.