CHATLOG

local log = function(plr,msg) --logging function
    print("<" .. plr.Name .. "> " .. msg)
end

for _,plr in next,game.Players:GetChildren() do
    if plr:IsA("Player") then --connect all current players to logging function
        plr.Chatted:connect(function(msg) log(plr,msg) end)
    end
end

game.Players.PlayerAdded:connect(function(plr)
    plr.Chatted:connect(function(msg) log(plr,msg) end) --connect all future joining players to logging function
end)