Why does this not face the part?

local target = workspace.THEPARTINEED
local camera = workspace.CurrentCamera
camera.CameraType = Enum.CameraType.Scriptable
camera.CameraSubject = target
while wait() do
    camera.CoordinateFrame = CFrame.new(target.Position)  --Start at the position of the part
                          
end

The camera is still but is not looking at the part?

Any ideas?

Scriptable camera will ignore both CameraSubject and Focus. It's whole purpose is to be fully controlled by your own code. This should work:

local target = workspace.THEPARTINEED
local camera = workspace.CurrentCamera
camera.CameraType = Enum.CameraType.Scriptable

while wait() do
    camera.CoordinateFrame = CFrame.new(target.Position, target.Position + target.CFrame.lookVector) 
end

Right now it will face same direction the part is oriented at, since I wasn't sure where exactly the camera should be located and where it should look.

Also consider using RenderStepped, since wait() is only 1/24 of a second, while roblox renders more often than that. Check these out:

http://wiki.roblox.com/index.php?title=API:Class/RunService/RenderStepped http://wiki.roblox.com/index.php?title=API:Class/RunService/BindToRenderStep

I'd personally use runService:BindToRenderStep(), otherwise do runService.RenderStepped:wait().