We propose a novel intervention to train the speed and accuracy of attention orienting and eye movements in Autism Spectrum Disorder (ASD). Training eye movements and attention could not only affect those important functions directly, but could also result in broader improvement of social communication skills. To this end we describe a system that would allow ASD children to improve their fixation skills while playing a computer game controlled by an eye tracker. Because this intervention will probably be time consuming, this system should be designed to be used at homes. To make this possible, we propose an implementation based on wireless and dry electrooculography (EOG) technology. If successful, this system would develop an approach to therapy that would improve clinical and behavioral function in children and adults with ASD. As our initial steps in this direction, here we describe the design of a computer game to be used in this system, and the predictions of gaze position from EOG data recorded while a subject played this game.