The correct version is:
Wir mussten leider feststellen, dass der Chrome-Browser einen Bug hat.
Here, we construct a compound from a browser further specified as Chrome.
Another possibility is:
Wir mussten leider feststellen, dass der Browser "Chrome" einen Bug hat.
Here, we're adding the name to the abstract term, and that's why I used quotes to make that clear, as e.g. in das Schiff "Titanic". Not absolutely necessary, as e.g. I'd write die Stadt Duisburg without the quotes.
Der Chrome Browser is wrong. The compound needs hyphenation.
But if I were to convey Chrome bug information, I'd write
Wir mussten leider feststellen, dass Chrome Version 123.456 einen Bug hat.
Without a version reference, the information is useless. Bugs show up beginning with one version, and get fixed in a later version. And I omitted the word Browser as the audience of such a statement surely knows that Chrome is a browser.