Is the pain always there?
Does it start up from step one or does it start up later in the run?
Is it there after the run?
The reason I ask is that it may be chemically based or injury based or even nutrient based.
Stretching may or may not help.
here's two links for calf stretching.
one is straight-legged for the gastrocnemius.
one is bent legged for the soleus.
you need to do two stretches to totally hit the calf.
I've got this too, and pretty bad in my left leg. I think it has something to do with putting stress on it. I got it shortly after starting boxing, where I keep most of my weight on that leg, and when I switch from foot to foot for skipping, it hurts like a bitch on my left leg. I get the pain behind my shin bone, and it's pretty localized. I pressed on it and saw stars from the pain. I went to the doctor and was supposed to mention it, but I forgot.
Pain is just weakness leaving the body. Stay alive, anyone can die. Pain is temporary, glory is eternal. Better to die on your feet than to live on your knees.
Why are you keeping most of your weight on one leg... only time I can think of most of my weight being on one leg is my back leg during a lead hook not often other than that... you orthodox or south paw?