yes, most probably. But the active one should also be apparent in chrome.
You could try using !important ie
.your-class {
border:5px!important;
}
But it is better practice to try to improve the importance by including more of the css cascade ‘tree’, not just the last bit .yourclass (start at #body or #wrapper if necessary).
However if !important works then your are going along the right lines
It would help to know which parent theme you are using……