Chrysler 300 C - What is the black thing right behind the plastic front bumper and the grill?

It's the bumper reinforcement panel. Depending on the body style, it is either aluminium or fibreglass. If you used the dimple marks on the bumper cover to mount your plate, there are matching holes in the reinforcement for screws to pass.

Chrysler 300 Bumper

I wouldn't listen to Joe. Chrysler isn't a bad Vehicle manufacturer. In reality, Chrysler is just as good as Mercedes-Benz due to the fact that the chassis, transmission, suspension, and several other parts come from Mercedes-Benz. So the reliability is the same as Mercedes-Benz. People just complain now just because they have nothing to do like Joe, never drove one and going off what their friends say, or they are just stupid.

But to answer your question, that is the Styrofoam behind the plastic on the bumper. There should be a Licence plate bracket to place the front plate on.

That is probably a Styrofoam spacer that most cars with that bumper cover have for some reason most likely by design. Most of these bumper covers will have 2 small indentations where the screws go for placing a license plate.

It's Chryslers' solid steal front bumper! Atleast, that's what they say it would be; Being the 2 timing scheisters' they are.