In Warhammer 40K does taking a Chaos Icon replace other weapons?
Does taking a Chaos Icon replace the model's boltgun? 


No.


  Can the model with the Chaos Icon replace his boltgun with a chainsword and still have that with an Icon of Chaos?


Yes. If a piece of wargear has to be swapped it will specifically say as much in the war gear entry. If it just says X models can take Y then you simply pay the points and they have the additional equipment.