This is a whole new area of learning for me. Despite examining many handkerchiefs over the years, I have never seen one like this. It is exceptionally embroidered and dates to the 1830-40's I believe.
I turned to Heather Toomer for information, and her book 'White-embroidered Costume Accessories; The 1790's to 1840's' [See Links & Research for full reference] has a small section which was invaluable when examining this piece. [See pages 176-185].
The first thing to explain that the word 'hankerchief' has a very different meaning in the 19th Century to that of the 18th Century. Here, in the 1830's, we are talking of the 'pocket' hankerchief, which came about after the Regency period when ladies gowns were too ephemeral to wear pockets [with contents] below their skirts. Along came the reticule, and around this time, pockets sewn into aprons etc. 
Toomer tells us: 'They were intended to demonstrate the wealth, position and taste of the owners.' Items of pure conspicuous consumption then.
Toomer also speaks of the finest embroidery, made by professional embroiderers, [much like the Master Embroiderers of the 18th Century] , using 'superb muslins'. The handkerchief would be held in the hand to show the World how grand the lady was!
Here is such a handkerchief. I cannot believe the tiny size of embroidery stitches, the range of fillings and the precise application of the design. All laid onto translucent fabric, as if to last for just a few hours before it melts away. And yet, here it is after 170 years!
You may also be interested to learn something the Lace Mentor told me - the fabric is actually linen. Despite having a sheen and appearing like silk. This quality linen thread was so fine that it could produce silk-like fabric [which of course is stronger than silk.]
The 'period' for these fine handkerchiefs seems to be the 1830-40's and so I am estimating that this one is the same [although it is smaller than the one's shown by Toomer]. This handkerchief came from Germany, and again, many seem to have come from Europe. 
A marvel for the embroidery collector. The size is 14.5" square.