That error message appears to be one specific to Chrome. It can occur for a number of reasons when Chrome thinks that the security certificate of a website is incorrect. One of them, of course, is that there really is something wrong with the website's security certificate. However if you're only filling in a competition entry (rather than doing something like online banking), there's still no need to worry.
Another cause of the problem could be that the clock on your computer is wrong. (So check it to ensure that the date's not incorrect).
The problem can also arise when you're using an antivirus program which uses its own 'https protection', blocking Chrome's attempts to keep you safe.
All in all though, for something which isn't 'high security' (as, say, online banking would be), I can't see any risks in using the site to enter a competition (or to take part in a promotion). If in doubt, try another browser.