Reliable in-hand manipulation requires accurate real-time estimation of slip between a gripper and a grasped object. Existing tactile sensing approaches based on vision, capacitance, or force-torque measurements face fundamental trade-offs in form factor, durability, and their ability to jointly estimate slip direction and magnitude. We present A-SLIP, a multi-channel acoustic sensing system integrated into a parallel-jaw gripper for estimating continuous slip in the grasp plane. The A-SLIP sensor consists of piezoelectric microphones positioned behind a textured silicone contact pad to capture structured contact-induced vibrations. The A-SLIP model processes synchronized multi-channel audio as log-mel spectrograms using a lightweight convolutional network, jointly predicting the presence, direction, and magnitude of slip. Across experiments with robot- and externally induced slip conditions, the fine-tuned four-microphone configuration achieves a mean absolute directional error of 14.1 degrees, outperforms baselines by up to 12 percent in detection accuracy, and reduces directional error by 32 percent. Compared with single-microphone configurations, the multi-channel design reduces directional error by 64 percent and magnitude error by 68 percent, underscoring the importance of spatial acoustic sensing in resolving slip direction ambiguity. We further evaluate A-SLIP in closed-loop reactive control and find that it enables reliable, low-cost, real-time estimation of in-hand slip. Project videos and additional details are available at https://a-slip.github.io.