The phrase to chop and change means to change one’s opinions or behaviour repeatedly and abruptly.

Here, chop originally meant to barter, and change meant to make an exchange with; in other words, this was an alliterative repetitive expression, the two verbs having roughly the same meaning (cf. also, for example, the alliterative phrase to be part and parcel of). In The Treasurie of the French Tong (London, 1580), Claudius Hollyband (floruit 1573-83), linguist and author, translated the French verb eschanger (contemporary French échanger):

Eschanger, to exchange, to chop, to scorse [= to barter].

The verb chop seems to be a variant of the obsolete verb chap, meaning to bargain, to trade, from the Old-English verb céapian, related to the Old-English noun céap, bargaining, trade, which is the origin of cheap and chapman.

The verb chop in this sense first appeared in chop-church, meaning church-chopper, attested in 1391 and defined by White Kennett (1660-1728), Bishop of Peterborough, in A Glossary to explain the original, the acceptation, and obsoleteness of words and phrases; and to shew the rise, practise, and alteration of customs, laws, and manners (London, 1816):

Chop-Churches. Those secular priests who drove a trade or made an advantage by exchanging of their benefices, against whom some constitutions were expresly [sic] made to restrain that mercenary practise.

The verb chop has also been used figuratively, especially in the phrase to chop logic, meaning to exchange arguments, to bandy logic. Probably under the influence of the homonymous verb chop, meaning to cut up, this expression has often been understood as meaning to ‘split hairs’, to ‘mince’, to ‘hash up’. The following is from A Treatise contayning a playne and perfect Description of Irelande, by Richard Stanyhurst (1547-1618), Irish literary scholar and translator, published in The Firste volume of the Chronicles of England, Scotlande, and Irelande […] Faithfully gathered and set forth, by Raphaell Holinshed (London, 1577):

Whereas you charge me with malpertnesse, in that I presume to chop Logike with you beyng Gouernor, by answering your snappish quid, with a knappish quo, I would wishe you to vnderstand, now, that you put me in mind of the distinction, that I as a subiect honour your royall authoritie, but as a noble man I despise your dunghill gentilitie.

The first recorded use of to chop and change, meaning to barter and exchange, is in A Morality of Wisdom, who is Christ, a mystery play written around 1485:

(1882 edition)
And I vse Iorourry [= jurory, defamation],
Enbrace questes of periury,
choppe and chaunge with symonye,
& take large yiftes [= gifts].

William Tyndale (circa 1494-1536), English scholar and Protestant martyr, used the phrase in the translation of the New Testament, as published in 1526; the Second Epistle of Paul to the Corinthians, 2:17, is as follows:

For we are not as many are which choppe and chaunge with the worde of god: but as they which speake off purenes / and as they which speake of God in the sight off God / so speake we in Christ.

In the King James Version (1611), this verse is:

For wee are not as many which corrupt the word of God: but as of sinceritie, but as of God, in the sight of God, speake we in Christ.

Very early, because the sense of the verb chop became indistinct, the meaning of the phrase passed from to barter to to change, alter; for example, in the Geneva New Testament (1557), the First Epistle of Peter, 2:2, is thus glossed:

And as newe borne babes desire^a the syncere mylke of the worde, that ye maye growe therby.
^a In this their infancie and newe comming to Christe he willeth them to take hede [= heed] lest for the pure milke, which is, the first begynnings of learning the syncere worde, they be not deceaued [= deceived] by them which chope and change it, and gyue poyson in stede of it.

As a consequence, the meaning of change passed over into chop alone. Probably under the influence of the homonymous verb chop in the sense of to strike in a given direction, as a nautical term, chop came to mean, of the wind, to change, veer or shift its direction suddenly. For example, in A True and Exact History of the Island of Barbados (1657), the business agent and natural science writer Richard Ligon (circa 1585-1662) wrote:

It was the time of Tornado, when the windes chop about into the South.

The British novelist William Makepeace Thackeray (1811-63) used the verb figuratively in The Four Georges. Sketches of manners, morals, court, and town life (New York, 1860); about George I’s accession to the British throne, he wrote:

If Swift had not been committed to the statesmen of the losing side, what a fine satirical picture we might have had of that general sauve qui peut among the Tory party! How mum the Tories became; how the House of Lords and House of Commons chopped round; and how decorously the majorities welcomed King George!