How to prevent someone from chatting?

Here is a link to the wiki article for SetCoreGuiEnabled(). This can be used in a local script to disable parts of the CoreGui interface. This however needs to be run from a localscript. I have used it before to disable parts of the CoreGui when a player enters (Like chat, and the health bar), but I don't believe it works if you run it in a LocalScript anytime while the player is in game.

-- LocalScript
game.StarterGui:SetCoreGuiEnabled(Enum.CoreGuiType.Chat, false);

This will disable roblox's core chat allowing you to completely script your own and if you make your own you can make it ignore players chats if the player is muted. This probably isn't what you're looking for, but I hope it helps.

If you mean only certain people can talk and not everyone do this..

local Talkers = {}

function Chat(Player, Message)
    for i,Talker in pairs(Talkers) do
        if Player.Name == Talker then
            -- Things here
        end
    end
end


game.Players.PlayerAdded:connect(function(Player)
local player = Player
player.Chatted:connect(function(Message)
Chat(player,Message)
end
end)

for i,Player in pairs(game.Players:GetPlayers()) do
local player = Player
player.Chatted:connect(function(Message)
Chat(player,Message)
end
end

Hope I helped! ;)