This is the scene from The Trial of the Chicago 7 (2020):
Did they allow smoking in the USA Courts?
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Now? No. Back then? Most likely. I am old enough to have had a job where we could smoke at our desk. Smoking was just a part of life, it was allowed on airplanes even. So, while I can't say for certain if it was allowed in courthouses, I can say based on my personal recollections that it most likely was in 1968 (when the events in the movie took place).
Given that you could smoke even in hospitals at around that time, this is an accurate depiction of courts of the era:
In the 1960s and even into the 1970s and ‘80s smoking was permitted nearly everywhere: smokers could light up at work, in hospitals, in school buildings, in bars, in restaurants, and even on buses, trains and planes
The laws have gradually changed since then, from allowing smoking everywhere to allowing it only in designated spaces to not allowing it anywhere indoors in public places, but this hasn’t always been enforced. Even as late as 1989 (alt link), one Florida courthouse had a haze of smoke in its hallways from all the smoking done inside it, against the rules.
The Chicago 7 were tried in the U.S. District Court for the Northern District of Illinois, a federal court, in 1969.
In 1972 the US Surgeon General proposed limits on smoking areas, but it wasn't until 1997 that President Clinton banned smoking in federal buildings via Executive Order 13058.
I worked in federal government buildings in the mid-90s and smoking was already not allowed indoors, though I'm not sure by what mandate. Society had changed by then and it was no longer considered acceptable to smoke in a crowded building even if there were no explicit rules prohibiting it.