The first answer is that humans cannot.
Chitin is a major component of the exoskeleton of insects and other arthropods, the cell wall of fungi and bacteria, the perisarco of hydroids and is also present in the epidermal cuticle or other surface structures of many other invertebrates. After cellulose, chitin is the most abundant naturally occurring biopolymer.
Chitin is a polysaccharide consisting of multiple units of N-acetylglucosamine (N-acetyl-D-glucos-2-amine) linked together with a bond-type β-1, 4, of the same glucose units forming the cellulose. Therefore, the the chitin can be regarded as a cellulose in which the hydroxyl group on each monomer has been replaced a group of acetilammina.
Pepsin in the stomach cleaves peptide bonds that bind together the amino acids of proteins, thus forming small peptides and amino fragments.
From the organoleptic point of view, chitin is considered a fiber, like cellulose and chitosans, suggesting it is indigestible.
Some herbivores, such as goats and some ruminants can digest cellulose, breaking them down long chains of polysaccharides. Similarly, echinoderms can eat shellfish, sea urchins and mussels and digest chitin, breaking mechanically only ones with hard shells.
However, hydrogen bonds between adjacent polymer guarantee the substance a remarkable hardness. This feature, combined with its flexibility and the fact that it is degradable by endogenous enzymes, chitin is an excellent material for the production of wires for surgical sutures, bandages and also synthetic leather. Chitin also has the unusual property of accelerating the healing of wounds in humans, closely related to chitosan (a more water-soluble derivative of chitin) and to the immune system of plants and animals.
EDIT
Yes, @mart. Echinoderms use chitin for producing proteins, similar to how herbivores use plant cell walls, which consist mainly of polysaccharides (non-nitrogen compounds), to produce the proteins (nitrogen-containing compounds), that serve us also (since we are not able to digest the grass).