SPACE CHASER / Taito / Arcade
Space Chaser appears to be Taito's odd space-themed take on Pac-Man (though I can't find the release month for it ... Pac-Man came out in April of '79 so this could possibly have been first.) You pilot a spacecraft through a maze picking up pellets, as what appears to be a heat-seeking torpedo relentlessly dogs you. At first you're like "pffft easiest game ever" because the torpedo starts so far from you and moves at roughly the same speed you do, so there's always a good gap between you and it. As you pick up pellets, however, it picks up speed, and when you're down to the last handful it really turns on the burners and chases you down mercilessly. You have just one trick up your sleeve, a limited burst of acceleration (denoted by the fuel gauge at the bottom of the screen), but which also has the side effect of draining your bonus points pool when used. It also only makes you go faster than the torpedo in the early going ... when the torpedo really ramps up at the end, it still goes a bit faster than you when you have the acceleration firing.
What the game ends up being about is route planning, making it more like a puzzler than the reflex-based style of a Pac-Man. Unfortunately that means that the game is really frustrating when you don't know the route (it's almost nearly impossible really), but once you figure out a workable route, you just use it over and over again, making it repetitive. I guess there's some replayability in trying to plan a better route and use less accelerant each time, though.
* Gameplay Video