Can Norton protect against spyware while using Chrome?

Seems it can't as I am always left with new cookies for Adviva, Burstmedia,casalemedia,doubleclick, fastclick, mediaplex after using Chrome for a few minutes..  these cookies don't get added using FF.  Whether that is Spybot immunization or Norton doing that I haven't checked.

 

Support told me if Norton was leaving them alone they could not be a threat, but fact is I don't want them there

 

I have been a Norton user off and on since the first Peter Norton Utilities came out back in the 80s. I am generally impressed the last few years...