Make a new .lua file (shadow.lua perhaps?) in the directory and put this in and then add the file name to the .toc of BasicChatMods. Play with the mode and offset if you're not happy, but that should put an outline with a 0 pixel offset on your chat. If you're using a pixel font then set the mode to 4.
Code:
local modes = {
nil, -- 1
"OUTLINE", -- 2
"THICKOUTLINE", -- 3
"OUTLINE, MONOCHROME", -- 4
"THICKOUTLINE, MONOCHROME", -- 5
}
local mode = 2
local offset = 0
local orig = {}
for i = 1, NUM_CHAT_WINDOWS do
local c = _G["ChatFrame"..i]
local font, size, flags = c:GetFont()
if not orig[c] then orig[c] = flags end
c:SetFont(font, size, modes[mode])
c:SetShadowColor(0, 0, 0, 1)
c:SetShadowOffset(offset, -offset)
end