We propose a new model for no-reference video quality assessment (VQA). Our approach uses a new idea of highly-localized space-time (ST) slices called Space-Time Chips (ST Chips). ST Chips are localized cuts of video data along directions that implicitly capture motion. We use perceptually-motivated bandpass and normalization models to first process the video data, and then select oriented ST Chips based on how closely they fit parametric models of natural video statistics. We show that the parameters that describe these statistics can be used to reliably predict the quality of videos, without the need for a reference video. The proposed method implicitly models ST video naturalness, and deviations from naturalness. We train and test our model on several large VQA databases, and show that our model achieves state-of-the-art performance at reduced cost, without requiring motion computation.