On the second of October , there was a game of cricket played at Wanborough [Illinois] by the young men of the settlement; this they called keeping Catherine Hill fair, many of the players being from the neighbourhood of Gadalming and Guildford, &c...-Two Years' Residence In The Settlement On The English Prairie, In The Illinois Country
This day [October 2, 1820] was kept at Wanborough, as last year, instead of Catherine Hill fair; but as some of the young men were gone to a county court at Palmyra, there was no cricket-match, as was intended, only a game of trap-ball. There have been several cricket-matches this summer, both at Wanborough and Birk Prairie; the Americans seem much pleased at the sight of the game, as it is new to them.
These references to cricket and trap ball, as I mentioned yesterday, are the oldest references that I'm aware of to ball-playing in Illinois. Given the sparseness of the population in Illinois prior to 1818, I would be pleasantly surprised to find a reference to a ball game that predates this one. I believe we still need to take a closer look at the 18th century French settlements in Illinois but nothing I've seen to date, other than the Gratiot reference, has been fruitful with regards to ball-playing among the early French settlers. The two earliest references that I know of that mention ball-playing in the Trans-Appalachian West date to the late 1790s and ball-playing references in the West prior to 1820 are rather rare. So the English Prairie reference is a significant one.
Two Years' Residence was written by John Woods and published in London in 1822. According to Robert Rogers Hubach's Early Midwestern Travel Narratives, "John Woods...was a British farmer who settled on the English prairie in 1819. His book gives a favorable view of conditions there and contains a full account of his life and much valuable information on social, economic, and political conditions in Illinois during 1819-1821. It includes notes on travel, agriculture, towns, and American customs." John Drury, in Old Illinois Houses, described English Prairie as "a semi-utopian colony of British immigrant-farmers" that was centered around Albion, Illinois, in Edwards County. The English nature of the settlers explain why they were playing cricket and trap ball, both well known English ball games.
I should also point out that the 1820 reference is the earliest, as well as one of the few, references to trap ball being played west of the Appalachians.
Note: The picture at the top of the post comes from the David Block's Baseball Before We Knew It site. Please don't sue me, David.