We present a first-of-its-kind ultra-compact intelligent camera system, dubbed i-FlatCam, including a lensless camera with a computational (Comp.) chip. It highlights (1) a predict-then-focus eye tracking pipeline for boosted efficiency without compromising the accuracy, (2) a unified compression scheme for single-chip processing and improved frame rate per second (FPS), and (3) dedicated intra-channel reuse design for depth-wise convolutional layers (DW-CONV) to increase utilization. i-FlatCam demonstrates the first eye tracking pipeline with a lensless camera and achieves 3.16 degrees of accuracy, 253 FPS, 91.49 µJ/Frame, and 6.7mm×8.9mm×1.2mm camera form factor, paving the way for next-generation Augmented Reality (AR) and Virtual Reality (VR) devices.