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The expression pecking order designates any hierarchy based on rank or status.

The primary meaning of this expression is: a social hierarchy amongst a group of animals (originally observed in hens) in which those of higher rank within the group are able to attack or threaten those of lower rank without retaliation.

The expression pecking order first occurred as a translation of the German noun Hackordnung in Social Life in the Animal World (London: Kegan Paul, Trench, Trubner & Co., Ltd., 1927), by the German zoologist Friedrich Alverdes (1889-1952), translated by K. C. Creasy—these are two extracts from this book:

[pages 123 & 124]:
Schjelderup-Ebbe * has shown how an order of precedence comes into existence within societies. A flock of fowls in a fowl run is not exclusive in the sense that its members make common cause against a new arrival, leaving the latter isolated. The new-comer may safely attach itself to the flock, but the position it is to hold therein must first be won by fighting. For no two hens ever live side by side in a flock without having previously settled, either for the time being, or for good, which is the superior and which the inferior; the “pecking order” thus established decides which of the birds may peck the other without fear of being pecked in return. Similar pecking codes exist, according to Schjelderup-Ebbe, among sparrows, wild ducks, and possibly among many other kinds of animals. Pecking among cocks is governed by the same rules as among hens, except that the cocks exhibit greater ferocity. Such “pecking orders” give the society concerned a certain degree of organization.
[pages 125 & 126]:
The tendency to form a social organization is innate in quite young chickens, whether or not they have been brought up with older fowls; it follows that the tendency must be purely instinctive and in no way dependent upon tradition. I think one can go even further and say that the instinct is, in a measure, indispensable to the very existence of social life among such animals (which, unlike the state-building insects, live mainly for themselves, and not for the welfare of the “state”). If this instinct failed immediately to establish a recognized order, such animals would pass their lives in a state of constant warfare, since their social instincts prompt them to seek one another’s company, while their self-assertive instincts urge them continually to attack one another. The “pecking order” is of great importance to the hens, for the superior bird is not disturbed when on the nest, nor robbed of its food, whereas it may disturb others and infringe their rights with impunity. The battles between hens or cocks are, therefore, not mere sport. A cock wields, in every case, despotic sway over all the hens, and will often interfere between two fighting hens, or even between two cocks which are attacking one another (provided, in this case, he is the superior of both the combatants). With penguins the case is different; for if the males fall to fighting, the females sometimes throw themselves between the antagonists and separate them.

* Thorleif Schjelderup-Ebbe (1894-1976) was a Norwegian zoologist and comparative psychologist.

The expression pecking order then occurred in the following from Point Counter Point (New York: Harper & Brothers Publishers, 1928), a novel by the British author Aldous Huxley (1894-1963) [chapter 26: From Philip Quarles’s Notebook, page 315]:

Since reading Alverdes and Wheeler I have quite decided that my novelist must be an amateur zoölogist. Or, better still, a professional zoölogist who is writing a novel in his spare time. His approach will be strictly biological. He will be constantly passing from the termitary to the drawing room and the factory, and back again. He will illustrate human vices by those of the ants, which neglect their young for the sake of the intoxicating liquor exuded by the parasites that invade their nests. His hero and heroine will spend their honeymoon by a lake, where the grebes and ducks illustrate all the aspects of courtship and matrimony. Observing the habitual and almost sacred “pecking order” which prevails among the hens in his poultry yard—hen A pecking hen B, but not being pecked by it, hen B pecking hen C, and so forth—the politician will meditate on the Catholic hierarchy and Fascism.

The earliest occurrences that I have found of the expression pecking order in the sense of any hierarchy based on rank or status are from “Where Will Mrs. Gann Sit?” Not Yet Settled, an unsigned article published in several newspapers on Sunday 27^th October 1929—for example in the Pittsburgh Sun-Telegraph (Pittsburgh, Pennsylvania, USA) [Magazine Section: page 9, columns 2, 3 & 6]:
—The following is about a formal dinner at the White House, in honour of Ramsay MacDonald (1866-1937), Prime Minister of the United Kingdom from June 1929 to June 1935:

“Where will Mrs. Gann sit?”
And who is Mrs. Gann, that it is so vitally important where she sits? Nobody elected or appointed her to any office. She is the wife of Mr. Edward Everett Gann, a Washington patent lawyer, which is of no importance because nobody cares where Mr. Gann sits. But she is also the sister of Vice-President Curtis, which caused all the trouble, because it had interfered with what scientists call, among hens, the “pecking order.”
Among wild fowl when the cock calls the hens to some food he has discovered, they always come to the meal in a fixed order of precedence. When a new hen joins the flock, if she can whip number one she becomes the first lady of that flock. If not, she breaks into the social dinner line wherever she finds a lady she can overcome. The State Department, for many years, has maintained a “Division of Protocol,” where etiquette experts were prepared to tell the wife of any official, high or low, just where she stood or, rather, sat in the Washington pecking order. […]
[…]
Had Mrs. Gann been the wife of the Vice-President instead of the sister, her position of number two in the pecking order would never have been questioned. Mr. Curtis, being a widower, assumed that as he had the power to choose his own wife, he could also nominate his sister as his hostess, and that she would be accepted everywhere as Lady Number Two.
[…]
Strange are the laws of etiquette as applied to the pecking order. Everyone agrees that Mrs. Gann’s dubious standing is because she is a sister, not a wife, to Mr. Curtis. It is the marriage relation that ranks one. But Mr. Gann is Mrs. Gann’s husband and yet that gives him no rank, precedence or rating at all. However, he has to be invited wherever Mrs. Gann is invited and neither he nor anyone else cares where he sits, though this is never among the seats of the mighty.