Can I reinstall CS3 on a new device?

I have CS3 installed on a laptop that is now very old and trying to die.  This is the second such laptop.  I'd like to reinstall it on a new one.  It is also on a home computer, therefore the license has been used the maximum amount of times to my understanding.  This would not be a third install, but more like a transfer.  Is this ok?  Will I encounter issues in doing this? 

Thanks