Try the following code. What this would do is convert the category taxonomy checkboxes to radio buttons. In this way only one category can be selected.
add_filter('wp_terms_checklist_args', 'wpse_64691_one_category_only', '', 2);
function wpse_64691_one_category_only( $args, $post_id){
$args['walker'] = new WPSE_64691_Category_Radio;
return $args;
}
class WPSE_64691_Category_Radio extends Walker {
var $tree_type="category";
var $db_fields = array ('parent' => 'parent', 'id' => 'term_id'); //TODO: decouple this
function start_lvl( &$output, $depth = 0, $args = array() ) {
$indent = str_repeat("\t", $depth);
$output .= "$indent<ul class="children">\n";
}
function end_lvl( &$output, $depth = 0, $args = array() ) {
$indent = str_repeat("\t", $depth);
$output .= "$indent</ul>\n";
}
function start_el( &$output, $category, $depth, $args, $id = 0 ) {
extract($args);
if ( empty($taxonomy) )
$taxonomy = 'category';
if ( $taxonomy == 'category' )
$name="post_category";
else
$name="tax_input[".$taxonomy.']';
$class = in_array( $category->term_id, $popular_cats ) ? ' class="popular-category"' : '';
if ( $taxonomy == 'category' )
$output .= "\n<li id='{$taxonomy}-{$category->term_id}'$class>" . '<label class="selectit"><input value="' . $category->term_id . '" type="radio" name="'.$name.'[]" id="in-'.$taxonomy.'-' . $category->term_id . '"' . checked( in_array( $category->term_id, $selected_cats ), true, false ) . disabled( empty( $args['disabled'] ), false, false ) . ' /> ' . esc_html( apply_filters('the_category', $category->name )) . '</label>';
else
$output .= "\n<li id='{$taxonomy}-{$category->term_id}'$class>" . '<label class="selectit"><input value="' . $category->term_id . '" type="checkbox" name="'.$name.'[]" id="in-'.$taxonomy.'-' . $category->term_id . '"' . checked( in_array( $category->term_id, $selected_cats ), true, false ) . disabled( empty( $args['disabled'] ), false, false ) . ' /> ' . esc_html( apply_filters('the_category', $category->name )) . '</label>';
}
function end_el( &$output, $category, $depth = 0, $args = array() ) {
$output .= "</li>\n";
}
}