The Color Chooser dialog does not remember its position between closing and re-opening it. It always appears in the dead center of the screen. Considering how helpful position-memory is, and how the Layer Effects dialog *does* remember its position, I think it's reasonable to request that the Color Chooser do so as well.
I'm trying out Designer with the hope that it can replace Illustrator. The software has been wonderful so far, but it's incredibly annoying that the Color Chooser plasters itself over the middle of my work every time I open it.