Actually, the same ads come up for everyone. When I was not premium, I had the same ad. Don't worry about it. It is just an awkward coincedence.
Chess.com is spying at you

You should get Norton or another cookie-removing software program and then get adblock for Firefox. theprez98 is right, it does work wonders.

If you used google, google tracks what you search for and sells that info to people who do ads, or gives it to google ads themselves. That way the money is most efficiently made.

Chess.com doesn't care where you are. But those who place the ads do. I'm surprised you noticed this only on chess.com, since you don't seem to be using of the other software mentioned and internet ads are everywhere.

Mekis is right. Internet is not secure. There are banners that will redirect you to unknown sites. If you enforce a strict security measure on your computer, you might not be able to log in to chessdotcom.
But there's no need to be paranoid. If you don't know about computer, there might be spywares inside your computer long before you join chessdotcom.
Even Microsoft do somekind of spying. That is the risk of running other people's program inside your computer. Legally, this is legal. Ethically, this is a delicate matter.
I just understood that Chess.com is spying on me. I have been looking for somewhere to live in Oslo, Norway. Going on vacation. So I was surfing the net, looking for a cheap place to live in. Then I went to Chess.com to play some chess, and guess what - every time I finish a game commersials for cheap hotels in Oslo turns up.
So Chess.com is spying on me, us. They see every move we take. This pisses me off, it is a crime against my freedom and my rights as a human being. Is the staff happy knowing about my erothic interests, where do my shopping and what I need?
I am finished playing here! And I advice you all to start thinking about what you are doing at the computer, because Chess.com staff knows all about it.
Maggie