Yes, when you are comparing times across time zones, you can use UTC time. (UTC is essentially a more modern GMT, there are differences but only the nerds care.)

You will want to use all times in UTC. But be aware that when you do this, any times that are meant to be the same throughout the year will shift one hour due to Summer Time/DST. Not every region does summer time, and the ones that do start and stop at slightly different times. (And Southern Hemisphere countries do it in Northern Hemisphere’s winter.)

If that’s too inconvenient for you, or most of your users are in your country, an alternative is to explicitly state the chat hours in your local time zone, with the understanding that it will shift a hour vs. UTC twice a year, and anyone outside your country’s summer time rules will just have to deal with it.