This can be an issue, even if you don't have chickens. Producing leafy vegetables and root vegetables in your garden can be especially problematic in those conditions. If you keep chickens, though, you have additional concerns. Studies have shown that chickens exposed to high environmental lead levels will have increased concentration in their own blood and body tissues, including their ovaries. When your chickens have high levels of lead in their bodies, this is communicated through their eggs to you.
We also know that the lead is particularly concentrated in the yolk. This is just not a good recipe for healthy living!
If you're looking for a good paint to use on your coop or nearby areas, modern paints and sealants free from lead are generally considered safe when dry (so long as they're not chipping). But if you're especially concerned, you might consider old-fashioned milk paint:
Milk paint is made with natural ingredients and pigments, and is environmentally safe and non-toxic.
On the other hand, if you think your area is already at risk for lead in the soil--or if you just want to make sure it isn't!--you may want to invest in a soil testing kit like this one:
Soil Testing Kit (lead in soil)
If you do find elevated levels of lead in your soil, you'll need professional advice to remove it for your safety, and the safety of your family and your animals.