UPDATE: Karan notes I have mixed some apples in with the oranges here. The block above is #2128 published as Double X #4 from the Ladies Art Company about 1890.
And Wilene notes the whole post is Wrong, wrong, wrong:
"This design has a long published history beginning as Unnamed in Farm and Fireside, March 1, 1897; then Edith's Choice in Hearth and Home, July 1896, and as Broken Dish the following month. Also again Unnamed in The Family published in Springfield, Ohio, October 1913; Cup and Saucer in Farm and Home, March 1, 1915; as unnamed friendship quilt in Oklahoma Farmer Stockman, ca. 1915-1920; Corn and Beans in Comfort, April 1923; Double X in Woman's World, April 1925; Sugar Bowl in Rural New Yorker, ca. 1930-1937; Wild Ducks in a June 1932 pamphlet from Needlecraft Supply in Chicago; Double X's by Nancy Cabot, April 10, 1935. All these have the square in the corner."
Here's a pattern that was quite popular about 1900-1920
This is a different block--note the corners are squares here, triangles above and below.
The block was often made up in blue and white.
A typical set of blocks in indigo blues
Other colors popular at the time were also used.
It's a rather odd construction, a square inside a square inside a square and then a strip of squares and triangles along the outside.
You don't find it any earlier than 1890 or so, the decade when these blue, gray and red quilts were so popular---also the decade when magazines began publishing quilt patterns. But I've never been able to find any published reference to it in the years when the design was fashionable.
This top may have been made between 1925 and 1950.
In 1930 Needlecraft Magazine published the design as Broken Dishes and in 1938 the Kansas City Star,
called it The Chinese Block Quilt. So it was published at least twice, according to my Encyclopedia of Pieced Quilt Patterns, but by the thirties new fad patterns had appeared and no one was very interested in making it anymore.
The mystery: How was it passed around in the 1890-1925 years if it wasn't published?
It was certainly popular enough. If you do an online search in the Quilt Index for the Chinese Block you find 15 different examples all made in that era (ignore the one dated 1865---it's misdated.)
Click here and type Chinese Block in the "Pattern Name" box and then search.
And the other mystery: What did the women who made it call it?
Here's a variation without the squares in the corners.
No published source or name for the pattern.
If you were looking to make a reproduction from the 1900-1920 period this would be a great design.
Rotary cutting instructions for a 12" finished block from BlockBase
A - Cut 4 blue squares 2-1/2"
B - Cut 4 light and 4 blue squares 2-7/8". Cut each in half with a single cut to make 2 triangles. You need 8 light and 8 blue triangles.
C - Cut 4 light rectangles 4-1/2" x 2-1/2"
D - Cut 2 blue squares 4-7/8". Cut each in half with a single cut to make 2 triangles. You need 4 blue triangles.
E - Cut 1 blue square 4-1/2"
F - Cut 1 light square 5-1/4". Cut into 4 triangles with 2 diagonal cuts. You need 4 triangles.
For setting ideas look at the variations at the Quilt Index. The blocks are usually set with sashing or alternate blocks rather than side by side.
I found this photo online in the 2004 records of the Iowa-Illinois Quilt Study Group.
With its lime green and Turkey red color scheme it might be late 19th century.
The biggest mystery here is why didn't I notice the detail of the corners in the blocks. All I can say is