On the init action, remove the action calling their function and enqueue an action calling your (differently named) function, like this:
add_action('init', 'wpse_80107_init');
function wpse_80107_init() {
// remove parent theme's header content action
remove_action('cyberchimps_header_content', 'cyberchimps_logo_icons');
// add child theme's header content action
add_action('cyberchimps_header_content', 'wpse_80107_logo_icons');
}
function wpse_80107_logo_icons() {
// your custom code here
}