Can I hide COREGUI for only one player?

You're going to want to use the SetCoreGuiEnabled method of the StarterGui.

In a LocalScript:

local Player = Game.Players.LocalPlayer
if not Player.Character then Player.CharacterAdded:wait() end

Player.Character.Humanoid.Died:connect(function()
    Game.StarterGui:SetCoreGuiEnabled(Enum.CoreGuiType.Chat, false)
end)

You'll still have to turn chat back on when they are spawned into the game, again from a LocalScript, but that code will disable the chat for someone that has died.