[Terranell]

I asked the same thing a while ago and mrruben5 and nightcracker helped with:

for i = 1, 7 do
    local chat = _G["ChatFrame"..i]
    local font, size = chat:GetFont()
    chat:SetFont(font, size, "THINOUTLINE")
    chat:SetShadowOffset(0, 0)
    chat:SetShadowColor(0, 0, 0, 0)
end

Just pop it in your BasicChatMods .lua file, or another addon's .lua or in it's own little addon.

You can comment out the two lines relating to shadow if you don't want the shadows.