In all likelihood, the flywheel or the clutch plate have uneven wear or some type of buildup on them. This is amplified when hot. The ultimate fix would require disassembly to figure out which one of the two is the culprit, but if you do that, you might as well replace both which will last you until you drive it into the ground. Personally, as it is only first gear and not the others, you may be able to let off the clutch with a slightly higher RPM in first to avoid as much chatter.
So my ultimate suggestion would be to live with it unless the vehicle is undriveable in first, in which case I suggest starting in second, which you can also do slowly enough to not stall the car with no gas. Obviously you'd want to put your foot on the gas when driving for real. What I'm saying is you can comfortably drive starting in second gear. I used to do it all the time when I lived out in Wisconsin because first gear would just spin the tires in the snow.