You did not provide the glue '/' in your implode call
<?php
$output = array();
$chunks = explode('/', $breadcrumbs);
foreach ($chunks as $i => $chunk) {
$output[] = sprintf('<a href="index.php?bc=%s">%s</a>',
implode('/', array_slice($chunks, 0, $i + 1)),
$chunk);
}
echo implode(' >> ', $output);?>