Agree with Foxy, she sounds broody to me. They lose feathers on their undercarriage so their skin is in contact with the eggs to warm them.
The white clumps usually look like granualted sugar at the base of the feathers and are very hard to get off - if you part the feathers you should also see fast moving yellow / brown coloured lice running for cover too.
A vet will often prescribe ivermectin drops or a pyrethium based powder for dusting. It soon removes them but the advantage of the ivermectin is it has a residual effect, lasting for 3 to 5 weeks or so. They usually advise a 7 day egg withdrawal period but I bet she isn't laying at the moment anyway.
I have moved your post to the chickens health section by the way ;-)
Oh and sorry - a warm welcome to the forum too...