I received a gomar at my old unit for a alcohol related incident but they decided to retain me. Can my new unit chapter me for it?

OK. 1. 1SG has lots of power and pull, but he doesn't decide on chapters. 2. If it is the past and has been paid for prior to the transfer, then it's not his responsibility. Talk to your CO on Open Door policy. Be truthful, if it has been overcome then tell him so. Your new 1SG would be like trying to court-martial you for something the old unit had handled with non-judicial punishment.

Here is the way it works.
You are assigned to let's say 1st Army HQ and you screw up for something alcohol related. Your commander at the time decides a GOMAR is sufficient. As long as you served the punishment as given and overcame it and all restrictions to include the bar, then when you PCS the new unit has jack all to say about it. You were punished and the incident is done and gone.

The gaining unit has to have a reason at THAT unit to initiate an unfavorable action. IE You have to have screwed up there and as long as you have not, your gaining unit has jack all they can do or say about it. They might not like that you got a GOMAR for alcohol but as long as you are not a repeat offender there is nothing to be said or done.

Use your units commander open door policy and talk to him. Also avail yourself of legal.

It's possible. You should talk to Legal about this. It's not the GOMOR your 1SG wants to chapter you for. It's the reason you GOMOR, the alcohol incident. Again, talk to Legal