The use of positron beam flow has a wide range of applications, and in this paper, we present the first on-chip positron accelerator based on dielectric laser acceleration. This innovative approach significantly reduces the physical dimensions of the positron acceleration apparatus, enhancing its feasibility for diverse applications. By utilizing a stacked acceleration structure and far-infrared laser technology, we were able to achieve a seven-stage acceleration structure that surpassed the distance and energy gain of previous dielectric laser acceleration methods. Additionally, we were able to compress the positron beam to an ultrafast sub-femtosecond scale during the acceleration process, compared with traditional methods, the positron beam is compressed to a greater extent. We also demonstrated the robustness of the stacked acceleration structure through the successful acceleration of the positron beam.