What is the chasm in the Arctic on Google satellite map?
You probably realise this, but you're not seeing that directly from satellite photos. Google Earth (or the "satellite" view in Google Maps) shows direct imagery on land, but underwater it shows a hillshaded view of bathymetry. So you're looking at the shape of the seabed.

With that said, I think this is the nothernmost part of the Mid-Atlantic Ridge, possibly the part known as the "Mohns Ridge". You'll see a similar line, coming and going, all the way from here down to the middle of the South Atlantic. There's a deep valley with mountains on either side. It's the boundary between two tectonic plates, where new seabed is slowly created as the Atlantic widens.

No, you should not be worried about it :-)