The phrase two is company, three is a crowd means that a third person is not welcome when two people—such as two lovers—want to be alone with each other.

The notion expressed by this phrase is first recorded in Proverbs communicated by Mr Andrew Paschall of Chedsey in Somersetshire, published in A Collection of English Proverbs Digested into a convenient Method for the speedy finding any one upon occasion; with Short Annotations. Whereunto are added Local Proverbs with their Explications, Old Proverbial Rhythmes, Less known or Exotick Proverbial Sentences, and Scottish Proverbs (Cambridge: Printed by John Hayes, Printer to the University, for W. Morden, 1678), by the English naturalist and theologian John Ray (1627-1705):

One’s too few, three too many.

The notion also occurs in A new Spanish and English dictionary: Collected from the Best Spanish Authors, Both Ancient and Modern. Containing Several Thousand Words more than any other Dictionary; With their Etymology; Their Proper, Figurative, Burlesque and Cant Significations; The Common Terms of Arts and Sciences; The Proper Names of Men; The Surnames of Families, and an Account of them; The Titles of the Nobility of Spain; Together with its Geography, and that of the West Indies; With the Names of such Provinces, Towns and Rivers in other Parts which differ in Spanish from the English. Also above Two Thousand Proverbs Literally Translated, with their Equivalents, where any could be found; and many Thousands of Phrases and difficult Expressions Explain’d. All the Words throughout the Dictionary Accented, for the ascertaining of the Pronunciation. To which is added, A Copious English and Spanish Dictionary Likewise A Spanish Grammar, more Complete and Easy than any hitherto extant: Wherein The Spanish Dialogues that have been Publish’d are put into Proper English. (London: George Sawbridge, 1706), by the English translator and antiquary John Stevens (circa 1662-1726):

Compañía, a Company, a Fellowship in Trade, a Society, a company of Soldiers.
[…]
Prov. Compañía de dos compañía de Diós: The Company of two is God’s Company. That is, two agree better than more, and may be truer Friends, and therefore their Society more pleasing to God.
[…]
Prov. Compañía de tres, no vále res: A Company consisting of three is worth nothing. It is the Spanish Opinion, who say that to keep a Secret three are too many, and to be Merry they are to [sic] few.
Prov. Compañía de úno, compañía de ningúno, compañía de dos Compañía de Dios; compañía de tres, compañía es; compañía de quátro, compañía del diáblo: One is no Company; two in Company God’s Company; three in Company is bare Company; these two have been explain’d above; four in Company is Company for the Devil; because four being just two and two may talk apart, and if they vary are just enough to Quarrel, and want an odd Man to reconcile them.

The earliest known occurrence of the phrase—as two is company, three none—is from a letter, dated 16^th November 1828, written by a woman signing herself Louisa Smith; published in The Citizen (Carlisle, Cumberland, England: Printed and Published by G. Irwin) of 1^st July 1829, this letter is one of the “verbatim copies” of replies that one ‘J. B. M’ and “another young man from Cumberland” received after “advertising for a wife” in several London newspapers:

I must tell you that under present circumstances I cannot introduce you to any young lady. How can I undertake to introduce a female friend to a person I know so little of (not even his name). Bye and bye when your friend has become acquainted with my family, then I might be enabled to say a good word for you to some of my fair friends, but until then you must excuse me, and remember two is company, three none, for we cannot say all we wish before a third person.

The current form of the phrase is first recorded in the review of Pictures of Europe, framed in Ideas (Boston, Massachusetts: Crosby, Nichols, and Company, 1855), by the U.S. Unitarian minister and Transcendentalist Cyrus Augustus Bartol (1813-1900)—review published in The North American Review (Boston, Massachusetts: Crosby, Nichols, and Company) of January 1856:

Travelling in company is obviously unfavorable to the flexibility, the enterprise, and the variety of a foreign tour. “Two is company, three is a crowd,” is almost as true of travel, as it is of conversation.

The following is from the description of the Dangler in Flirtation Corner, published in London Society. An Illustrated Magazine of Light and Amusing Literature for the Hours of Relaxation (London, England: Printed by W. Clowes and Sons) of August 1865:

As a third person singular in Flirtation Corner, where ‘two is company,’ he hath not his equal.

A variant of the phrase, with the word trumpery, occurs for example in Chapter XIV of Monica. A Love Story of Modern Days, published in The Indiana Democrat (Indiana, Pennsylvania) of 29^th May 1884:

“Why was I to be deceived?” says Monica. “I think I have been very basely treated. If you, Kit, desired a clandestine meeting with Mr. Desmond, I don’t see why I was to be drawn into it. And it was a stupid arrangement, too; two is company, three trumpery. I know, if I had a lover, I should prefer—”