Of American-English origin, the humorous informal noun cackleberry denotes a hen’s egg. It is composed of cackle, denoting the raucous clucking cry given by a hen, especially after laying an egg, and of berry¹.

¹ In Old English, berry was chiefly applied to the grape, since the word denotes any small roundish juicy fruit not having a stone, as opposed to apple, which was in Old English a generic term for all other kinds of fruits, including even nuts. In fact, berry and apple are the only Anglo-Saxon fruit names, the rest being of Latin or ‘exotic’ origin—cf. origin of the phrase ‘the forbidden fruit’ and the apple of one’s eye – la prunelle des ses yeux.

The earliest instance of cackleberry that I have found is from the menu of the annual banquet of the Oakland Canoe Club, published in the Oakland Daily Evening Tribune (Oakland, California) of Saturday 2^nd February 1889:

Entrees (a la Hasslocher)—Salmi² of Malard [sic] Duck with Olives, Chicken Curry, and Rice.
[…] Chippy [= chipping sparrow] on Toast. Painter [= panther?] red. Scrambled Brains. Grizzly Bear (a la totem). Cackleberry Tarts turned over (a la Gump³).

² The following definition is from The Encyclopædia of Practical Cookery (London – 1892), by Theodore Francis Garrett and William A. Rawson:

Salmi or Salmis—A name given to a ragoût of partly roasted game, stewed with sauce, wine, bread, and condiments, suited to provoke appetite.

³ Here, gump is perhaps the slang noun for chicken first recorded in 1914 only by the Oxford English Dictionary (2^nd edition, 1989).

The second-earliest instance that I have found of cackleberry is from one of the unconnected short paragraphs of local, miscellaneous news on the last page of the Hill City Democrat (Hill City, Kansas) of Thursday 27^th March 1890:

Spring house cleaning is here.
Our merchants report trade increasing.
A week from next Sunday is Easter Sunday.
Lafe C. Smith, of Stockton, was in this city last Tuesday.
The local market is well nigh glutted with cackle-berries.
There was considerable activity in real estate the first of the week.
This system of subscribing much and paying little is what breaks the preacher’s and editor’s hearts.
[&c.]

In the following humoristic paragraph from Local Notes, published in The Princeton Union (Princeton, Minnesota) of Thursday 12^th August 1897, hen fruit is used as a synonym of cackleberries:

There was an episode on the streets Tuesday evening which was not very creditable to the participants. A traveling phrenologist was lecturing in open air and took occasion to censure a part of the audience who were standing on the sidewalk. His language inflamed some of the hot heads and a moment or two later a gust of wind wafted a few specimens of antiquated cackleberries in the direction of the speaker’s head and the strength of this argument convinced the audience that a more pleasant place could be found at home. A “gentleman in the audience” whose bosom arrested the course of one of the pieces of decayed hen fruit applied a few choice epithets to the perpetrators and threatened to do some shooting but the coroner has not yet been called.