Sorry...I should have indicated that in my post...I got one when my character reached lvl-18 (I think...somewhere around that level anyway)...but wondered/hoped there might be a way to craft more, later on when I'm able to get crafting skills to higher levels...or are they limited to the store after getting the reward via leveling?

There are a total of 4 60 slot and 4 30 slot storage containers that can be placed in housing. The level 18 reward is one of the 4 30 slot containers. They can be bought from the crown store as you noted, but also from Faustina Curio (one of the two NPCs who sells things for writ vouchers). So although they can't be crafted themself, a high level crafter can generate a fair number of writ vouchers over time and buy them that way with.
If you're completely new, writ vouchers are a currency mostly earned by doing master crafting writs; master crafting writs drop randomly from top level daily craft writs.

BTW just in case it's unclear there are 8 storage chests in total.

1 is only from the level up rewards and the other 7 can be bought with crowns OR writ vouchers OR tel var stones. Don't make the mistake some people have of getting the crown ones first thinking they'll get 8 more with writ vouchers later.