Remove the string concatinator (..) after the comma, and GetText is a function value so it needs to have (). So:
chat.AddText( Color( 0, 255, 0 ), "(ADMIN)", Color( 0, 255, 0 ), ..TextEntry:GetText )
Should be:
chat.AddText( Color( 0, 255, 0 ), "(ADMIN)", Color( 0, 255, 0 ), TextEntry:GetText() )