"The liver is not in the chest."
Translation:Die Leber ist nicht im Brustkorb.
Good question, but it sounds definitely odd. I would expect to read this order in a poem to create a rhyme with -icht, but not in a normal conversation.
I think when you're negating a sentence which gives a position, you negate the location itself, because ultimately the thing you're talking has to be somewhere, so negating the verb sounds weird.