I contacted the Chinese Consulate in Chicago and they told me visitors no longer need a letter of invitation. Reading between the lines, it seems like the policy was a temporary one put in place during the phase leading up to the Beijing Olympics in 2008.
That makes the somewhat arduous process of getting a China visa (US$ 130 for single or multiple entry for US citizens) a little less so. So this is good news. However, if the policy changes, here’s some information on how to get the invitation letter and what needs to be included in it.