So instead of Raditz coming to Earth, Master Chief crash lands in the DBZ world.
MC thinks Goku is a hostile alien and attacks. He is alone on this world with no backup. He has the Cortana AI but she works for 30 seconds until she shuts down completely so he has to use it sparingly.
He has a Spartan Laser, a battle rifle and 1 plasma grenade.
Goku has not yet had training with King Kai so he doesn't know the Kaio-Ken nor can he turn Super Saiyan.
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Alright here's how I see it. Master Chief uses Cortana to create a dimensional portal. He goes into the Halo dimension and Goku follows him. Master Chief uses his evasive tactics to make his way to the Composer. He activates the Composer and destroys Goku. I'd say the odds are about 99:1 in favor of Chief.