Rats eating eggs and two hatchlings??!

[FatChicksDigMe]

Hi guys,

I think I have a rat infestation! I have been dealing with egg eating hens for a month now (and I caught some in the act that's how I know it's them) but this morning I'm not so confident if they are the only one.

I have three eggs under a broody silkie and a helping Brahma that were ready to hatch but when I went to check on her yesterday one egg was missing without a trace. I was confused and disgusted thinking that maybe one of the egg eating hens took their cannibalism to the next level but this morning I checked under both girls and found shell fragments. I searched for the chick and couldn't find it anywhere. Upon closer inspection I saw rat poop in the nest...

So I think there's a rat eating my hatchling Two more things to note, before checking on them I heard the rat somewhere on their roof chewing something and I banged my fist to try to scare it so that I can see it scurry. It just was quiet after that. Also, yesterday I found rat poop in another nest alongside a broody

 

[FatChicksDigMe]

Ok, so I started to clean on top of the chicken run and removed the waterproof tarp over it and found the rats likely nest with poop everywhere.

My question now is how do I safely dispose of their feces so that it doesn't contaminate the soil for my chickens!? I also doubt want the girls to eat the poop either as they can be a little dense sometimes (i.e eating pine bedding when they know better)