The universe is made up a infinite parallel timelines where there are small differences between adjacent timelines but the differences get larger the farther from the base time line you travel. The main character is human who is able to speed himself up (hyper speed?) for short periods of time. He is working for a high tech race of lizards (descended from dinosaurs?) who are trying to dominate all the parallel timelines. read this sometime in the early 1980's
Thanks for the suggestion of Orion by Ben Bova but this isn't it. The travel between timelines is done with machinery and the hero's ability to to increase his speed was also an implanted system. The hero starts out working for the Lizards then ends up fighting against them. The opening chapter starts (if I remember correctly) with the hero trying to steal something out of an office in a house (maybe) and having a shoot out with the guards. He is able to move much faster than the normal humans but is hampered by the pistol that he is using can't operate as fast as he can pull the trigger.