This paper presents a novel approach to acquire multichannel wireless intracranial neural data based on a compressive sensing scheme. The designed circuits are extremely compact and low-power which confirms the relevance of the proposed approach for multichannel high-density neural interfaces. The proposed compression model enables the acquisition system to record from a large number of channels by reducing the transmission power per channel. Our main contributions are the twofold. First, a CMOS compressive sensing system to realize multichannel intracranial neural recording is described. Second, we explain a joint sparse decoding algorithm to recover the multichannel neural data. The idea has been implemented at system as well as circuit levels. The simulation results reveal that the multichannel intracranial neural data can be acquired by compression ratios as high as four.