[support] Dynamically display parent/child taxonomy terms in a separate list?

[Paul Kim]

Is there a way to display a single-hierarchy taxonomy terms separately? 
For example, if we have this list:

Parent1
--child1
--child2
Parent2
--child3
--child4
--child5

I want to show two drop-down menus, populating the first one with:

Parent1
Parent2

Once a selection is selected in this first drop-down menu, a second 
drop-down menu is populated with the children based on the selection of 
the first drop-down menu. What's the best way to do this?

Thanks!