How to Stop Style.CC for Being Overrided

I am looking to manually modify some CSS styling on the navigation menu etc. When I add the CSS code to the themes style.css or the Child theme's style.css it will not override what is listed in the core theme's style sheet.

For example:
Modification added in style.css
.main-navigation {background-color:green;} // Does not take affect and is overwritten

Theme's Original Code

<nav itemtype="http://schema.org/SiteNavigationElement" itemscope="itemscope" id="site-navigation" class="main-navigation">