What breed is this hen?

[debid]

Yes, she's more then likely a Black Sexlink.

A sex link is a chicken that is bred a certain way so the Sex can be Determined at Hatch. Rhode Island Red Rooster over Barred Rock hen produces the Black Sexlinks.
Males hatch with head spots, & feather out Barred, the Females hatch out Black with leaky red in face, & feather out unevenly colored with black, red/gold coloration.

This. There are other combinations that also work. You can take a guess based on her physical traits but you can't really be sure. The way hatcheries prioritize production, it's more likely they used a production red rooster. I can be sure of that with mine because her gold is so light, it's almost buff and her neck is spotted.

 

[Not-so Slick Chicken]

I see, so what do you think this exact bird is? A Black Sexlink? What does that mean. I'm assuming a cross breed chicken? If so, of which breeds?

Assuming that store used hoovers, that hatchery's black sex-links are Rhode Island Red rooster x Barred Plymouth Rock hen

Hatcheries/breeders tend to like to keep some things secret, but certain common crosses are sometimes disclosed.