Valor Chests can be earned both as a reward from the Path of Valor and by continuing to collect Valor Points even after all Milestones have been reached.
There is a bar under the "Rewards" tab in the Path of Valor menu. Once the player has reached the 30th Milestone, the bar will begin tracking additional Valor Points earned. For every 1000 additional Valor Points, the player will earn a Valor Chest. At the end of each Path of Valor, all collected Valor Chests are automatically claimed and Valor Points are reset to 0.