Is the chitin in an insect's exoskeleton cross-linked?
much like cellulose, chitin strands are bonded to other strands by hydrogen bonds. here is a slide share with a breakdown of the structure. 

It is crosslinked in the sense strands are linked to other strands in such a way that most enzymes cannot access it to break it down. this is the same thing that makes wood last untreated. In a strictly chemistry sense it is not a crosslinked polymer (which requires covalent or ionic bonding) but it still has crosslinking. Your hitting a difficulty in jargon. 

source.