While a chalk bag is not a requirement for bouldering or climbing in general, it is highly recommended to use chalk as it can be the difference between sending a route and falling. Chalk, when used, is preferably kept in a chalk bag or a chalk bucket, which is similar to a chalk bag, just larger and usually with more pockets for brushes and other items.
Chalk can be essential for those who sweat from their palms, or that climb with others who sweat, since they may be causing the climbing holds to be more slippery for you as well as for them.
Many people also don't think that they sweat from their palms and that they do not need chalk, but, most don't realize that they sweat even slightly, and that small amount of sweat could be what causes you to slip from a hold and not send the route.
