The Famicom version never saw a port to the NES. I wish it would have because it allowed use of the Arkanoid rotary controller for steering the vehicle in Chase H.Q. Probably the only home port of this game that allowed a rotary steering controller option.
That is a really cool idea! A bit like the way you can use the paddle controllers for the Atari versions of Night Driver.
Two options: Buy a Japanese Famicom setup and its Chase H.Q. game, along with a Japanese Arkanoid controller. Or, buy a Famicom to NES adapter and a Famicom Chase H.Q. cartridge, along with a NES Arkanoid controller. I think the second option makes most sense to me since I already have the Arkanoid controller.