[Bob KellyIII]

I have seen spacers on the rear tire/axle that are slightly different in length
I have no idea if that is the case with your bike or not but if it is it's an easy fix
just pull the axle and the spacer on each side of the rear wheel and see if they are the same width.... if one is longer it probably belongs on the right side
.... the wheel alignment is top priority, I have ran a Old Honda 90 for thousands of hours with the chain running off to one side but it worked fine
it bugged me one day so I aligned the chain and sprockets despite the alignment marks on the rear swingarm and took it for a short ride....
when I returned I aligned the wheels not the chain !!! it would wallow in the corners and make your butt pucker big time not something you want to experience on a faster bike for sure !
Bob.........

edit; something must be amiss somewhere because both the chain and the alignment should be spot on at all times they were made to do that
so if your's is noticeably out of alignment with the sprocket when the wheels are aligned I'ed say you did something wrong somewhere
I mentioned the spacers for a reason , many times they interchange real easily and a person won't notice it at all. I think the DT1 Yamaha has
a 2" spacer on one side and a 1/4" spacer on the chain side you can mix them up but nothing will fit right, but it's a bit tougher when it comes to better street bikes the spacers look identical most of the time but ARE THEY ? that's the big question .... if their identical in thickness and can be swapped from side to side there's no problem ...but you need to know or pull it apart and check yourself because you could have swapped them without noticing it. and that may well be the cause of the wheel alignment being correct but the chain isn't ( rides to one side on the rear sprocket)