Freezing won't affect the nutritional value at all, but if you put hot chicken stock in the freezer it might affect the texture of everything else in the freezer! I'd advise cooling your stock quickly with ice water (or at least tap water) before you freeze it.
As above, you can concentrate it a bit more by putting it over heat again. Boiling it will evaporate water faster than it will degrade the gelatin, so you'll be left with even more concentrated stock than you currently have.
I freeze mine in muffin trays for a few hours, and then transfer into plastic bags. Each muffin-shaped block is about 200mL, which makes it useful for making sauces without having to thaw an entire container of stock.
"Thanks to the combination of meat, calcium-rich leaf foods, and a vigorous life, the early hunter-gatherers were robust, with strong skeletons, jaws, and teeth." - Harold McGee, On Food And Cooking: The Science and Lore of the Kitchen