I just bought a power antenna with a red wire, a blue wire, and a ground wire. Problem is I have the original relay wiring with white, green, and grey wires.

Do you just connect the red to white, the blue to the grey, and leave the green wire alone?

Doubt that would work , , you would only have power in with no ground path
Would appear green is the common ( ground ) back through the relay
See
http://92b4crs.tripod.com/86wiring/dia-pics/151-0.jpg

I thought about that, but the instruction manual said to ground it to the chassis (it has a black ground wire), so I figured grounding it to the chassis would make the green redundant. Do you think I should connect the black ground wire to the green? I guess it seems to make the most sense.

One way to fine out
Wire it up according to the instructions and see if it works

If you look at the factory diagram it goes up with power on the white and ground on the green.
To go down it puts power on the green and ground on the gray to reverse the motor