Corebook handles chases two ways: with a simple competitive check and with a check at the beginning and a full turn for everyone involved. If I go with the first, will you allow maneuvers to happen? Like, I Punch It to go faster and then make the skill check, or use two maneuvers to accelerate and then the skill check.

Once you're involved in a chase, you can use manoeuvres for everything you otherwise can, EXCEPT to increase or decrease the distance between the ships involved. You can use Punch It! and/or manoeuvres to increase the speed, and then that comes into play if you win the competitive Piloting check between rounds (winner changes distance by one range band plus one for every Speed difference).

Oh I see what he's saying! The Chase mechanic is one way, but under the skills listing for Piloting it also says you use Opposed checks (not Competitive).

GM's call.

My opinion is:

The Chase Mechanic is what you roll for a formalized ongoing chase in an Initiative encounter. Say pursuing an Imperial Scout ship before it can report in as part of a planned encounter in an adventure, something that should take a few full rounds with lots of action.

The Opposed check is what you make in a more informal chase where you wouldn't go into initiative. Like pursuing the pickpocket that stole your blaster in a more random encounter not directly connected to the larger adventure plan, something that might just be a roll or two and then over. So maneuvers wouldn't be tracked because it's not that kind of encounter.