Will be in NYC on Monday June 28th. I know there is an 8pm performance of Chicago that day and wondered if I should get tickets ahead or will I be able to get them at the discount booth.
Have only been to the theatre on weekends and don't know if it's less busy on a Monday.
Any help is appreciated! Thanks.

The answer to getting them at TKTS is a meaningless "probably". Here's another idea. It's too early right now for June, but in another couple months you can go on line to any of the online discounters -- www.theatremania.com, is a good one. There you can preorder tickets at a 40% discount. Not quite half price, but worth it to be sure of getting good tickets in advance. Currently they only offer that deal through March 18, but it will be extended as the run goes on.

Patrick has given good advice. There probably won't be any special offers for late June until early May at the earliest.
Monday night is a fairly quiet night for NY theater, so you would have a fairly good chance of getting tickets...but no guarantee, of course.

Is the TKTS booth even open on a Mon since most theaters are dark?

Yes, it's open on Mondays.