Chagrin Valley has a bit of a confusing history, often noted as a Stanley Thompson design. The following blurb is taken from the Case Western Reserve Encyclopedia of Cleveland History.
The description of the location of the course accords with this 1927 Map and the modern aerial of the course.
The hard part is figuring out exactly what was built, when and who did it.
In 1923 the club had 9 holes with plans for 9 additional holes.
April 1, 1923 Cleveland Plain Dealer -
This 1924 article discussing the addition of 9 holes (and eventual planned expansion to 36 holes total) notes the course was laid out by Stanley Thompson. What is unclear is if this refers only to the 9 hole addition or the entire 18. If Thompson did lay out the initial 9 holes that existed in 1922, it would most likely be his earliest work in the United States. All of the dates in these articles seem a bit off from the dates provided in the Encyclopedia entry above.
April 6, 1924 Cleveland Plain Dealer -
As the Encyclopedia article notes, part of the Chagrin Valley course was taken over by Moreland Hills CC. Prior to that, the portion of the course on the east side of SOM Center Road was leased to the Cleveland arm of the National Town and Country Club, a national organization with branches in a number of cities. NT&CC would use this land for a few years before moving on to the old Country Club (who had moved to their new location at Pepper Pike) site at Bratenahl, where it was succeeded by the Lake Shore CC. NT&CC also built an opulent city club which remains today as Fenn Tower, a dormitory at Cleveland State University.
March 28, 1928 Cleveland Plain Dealer -
March 29, 1931 Cleveland Plain Dealer -
Chagrin Valley itself continued on with a full 18 hole course, the new (third) nine holes opening in 1928 (I can find no record of who designed this 9). What is hard to decipher is which of the first two sets of 9 holes were turned over to NT&CC and Moreland Hills.