Yes, the monthly archives read in reverse chronological order, and there's no way to change that directly. (And the monthly archives don't display your posts anyway: they display a list of months only; clicking on a month brings up a dynamic page with the posts published that month - again in reverse chronological order.)
If you want monthly archives displayed in chronological order in the sidebar, the only way to do it is create a custom list in a text widget. If you want a list of your posts in chronological order, you can do it in a static page. The drawback in both cases is that you'll have to update the list manually.