Wild chicken, need help identifying

[BiomeBob]

Good evening. Over the last couple weeks, this chicken (@ first we thought it a fighting rooster from distance) started showing up. It stayed a distance away from our chickens, but now hangs around with them as they range. Often shows up (like today), sometimes doesn't. IT FLIES - has launched itself fom tree to tree and a distance over the fence.
Searching, thought it could be an Ancona, but not sure (no white specks)

Can anyone please help identify it?
Not sure anymore that we want to catch it up and keep it.

 

[BlueBaby]

It look's to be some sort of game hen to me.

 

[Ducksandchickens]

First off where are you located? Not exact just the general idea.

 

[BiomeBob]

EGG EATING - Also, since it's arrival, noticed eggs had been eaten yesterday from pen (it has walked into pen a number of times). But searching threads, looks like egg eating could be a 'normal' thing among chickens.
We wanted to try catching and keeping with the others, but since the egg eating thing started, probably not
We’ve got our four hens in the pen for awhile, due to digging up where we’ve been or trying to plant garden/seeds, including by this wild one.

 

[BiomeBob]

We're in Chaparral, NM, outside of El Paso, TX. Desert area.

 

[BlueBaby]

If that visiting one is eating your egg's, then it will continue to do so as long as you leave easy access for it to get in there to the nest.

 

[BiomeBob]

If that visiting one is eating your egg's, then it will continue to do so as long as you leave easy access for it to get in there to the nest.

Yeah, no we've secured the other ones inside the pen for now, so there's no way the visiing one can get in there.

 

[Amer]

Yeah some kind of game hen

 

[RoostersAreAwesome]

She's an American game hen

 

[RoostersAreAwesome]

EGG EATING - Also, since it's arrival, noticed eggs had been eaten yesterday from pen (it has walked into pen a number of times). But searching threads, looks like egg eating could be a 'normal' thing among chickens.
We wanted to try catching and keeping with the others, but since the egg eating thing started, probably not
We’ve got our four hens in the pen for awhile, due to digging up where we’ve been or trying to plant garden/seeds, including by this wild one.

She might be eating eggs because she's starving. Chickens usually don't survive that long in the wild.