We present a novel method of CNN inference for pixel processor array (PPA) vision sensors, designed to take advantage of their massive parallelism and analog compute capabilities. PPA sensors consist of an array of processing elements (PEs), with each PE capable of light capture, data storage and computation, allowing various computer vision processing to be executed directly upon the sensor device. The key idea behind our approach is storing network weights "in-pixel" within the PEs of the PPA sensor itself to allow various computations, such as multiple different image convolutions, to be carried out in parallel. Our approach can perform convolutional layers, max pooling, ReLu, and a final fully connected layer entirely upon the PPA sensor, while leaving no untapped computational resources. This is in contrast to previous works that only use a sensor-level processing to sequentially compute image convolutions, and must transfer data to an external digital processor to complete the computation. We demonstrate our approach on the SCAMP-5 vision system, performing inference of a MNIST digit classification network at over 3000 frames per second and over 93% classification accuracy. This is the first work demonstrating CNN inference conducted entirely upon the processor array of a PPA vision sensor device, requiring no external processing.