I have just downloaded Chrome and was able to download and run mIRC through it without any issues.

The most common reason for this type of message is anti-virus software that incorrectly thinks that mIRC is a trojan/virus, perhaps because they have not updated their signatures database. This is called a false-positive. You would very likely need to add an exception for mIRC in your anti-virus software and if that does not work, report it to the anti-virus company so that they can tell you how to resolve the issue.