Sex

Sex, in Objectivism, is a response to values rather than a purely physical appetite: Ayn Rand held that a person's sexual desire is set by his deepest convictions about himself and about what is worth admiring, and that sex is therefore an expression of self-esteem rather than a means of acquiring it.

“The fact that a man's sex life is shaped by his conclusions and value-judgments is evident in every aspect. It is evident in the setting he prefers, the state of dress, the caresses, positions, and practices, and the kind of partner. This last is particularly eloquent.”
~ Leonard Peikoff, Objectivism: The Philosophy of Ayn Rand, chapter 10

The argument

Rand's view of sex is a case of a wider position: that emotions are not primaries but responses to one's value-judgments, which in turn rest on what one knows and believes. See Emotions and Value.

Applied to sex, this gives a specific claim. Physical desire in a human being is not directed at a body considered as an object; it is directed at a person, and what makes that person desirable is the traits one has already judged to be admirable. A man who holds achievement, independence and integrity as virtues will respond to someone in whom he sees them. A man who holds nothing in particular will find sex correspondingly empty, because there is nothing for it to be an expression of.

The reason this matters to the ethics is the direction of causation. Sex, on this account, is an effect of a man's estimate of himself, not a way of producing one:

A man who regards himself as competent to live seeks a partner he considers worth winning, because only that gives the experience any meaning.
A man who despises himself and pursues sexual conquest for self-esteem is attempting to gain a value by seizing its consequence, which is the same error as expecting wealth without production. It fails for the same reason.

“But, in fact, a man's sexual choice is the result and the sum of his fundamental convictions. Tell me what a man finds sexually attractive and I will tell you his entire philosophy of life.”
~ Ayn Rand, Francisco d'Anconia to Hank Rearden, Atlas Shrugged

Against the soul-body split

Rand presented this as an application of her rejection of the mind-body dichotomy. The traditional view she was arguing against treats sex as a concession to the animal in man — at best tolerated, at worst a debasement, and in either case unrelated to his spiritual life.

Objectivism denies the split. Man is an integrated being, and the physical is the form in which values are experienced rather than a rival to them. On this view sex is not something to be excused; it is a celebration of oneself and of existence, which is why Rand treats a person's sexual life as evidence about the rest of his philosophy rather than as a separate compartment. See Mysticism and Faith for the tradition she is answering.

The theme is dramatised throughout Rand's fiction, notably in the contrast between Hank Rearden's marriage to Lillian and his relationship with Dagny Taggart, and in Francisco d'Anconia's explanation of the subject to Rearden.

Common misunderstandings

That it prescribes a particular kind of partner or practice. The claim is that sexual response is caused by one's values, not that Objectivism issues a list. Rand's remarks on which traits she personally found admirable are her judgments, not deductions from the philosophy.
That it makes sex a duty or a test. Nothing in the position obliges anyone to have sex, to want it, or to treat frequency as a measure of virtue.
That Rand's views on gender roles follow from the philosophy. Rand held some strong and specific positions on masculinity and femininity, most famously in "About a Woman President". Many Objectivists regard those as personal opinions inconsistent with the rest of the system rather than as part of it, and this is an open and much-argued question rather than settled doctrine.
That the scene between Roark and Dominique in The Fountainhead endorses rape. This is the single most common objection raised about Rand and sex. Rand is reported by Barbara Branden to have described it as "rape by engraved invitation" — that is, as a consensual encounter written in the idiom of romantic fiction. Whether the text supports that reading is disputed, including among readers sympathetic to her.
That sexual desire being value-driven means it is chosen. The values are chosen; the response is not chosen at the moment it occurs, any more than any other emotion is. This is why Rand treated sexual attraction as diagnostic — it reports convictions a man may not have stated to himself.

Discussion

References

Rand, Ayn. Atlas Shrugged — Francisco d'Anconia on sex, in the chapter "The Sanction of the Victim".
Rand, Ayn. "About a Woman President", first published in The Objectivist (1968), reprinted in The Voice of Reason.
Branden, Barbara. The Passion of Ayn Rand. Doubleday, 1986 — source for the "engraved invitation" remark.
Peikoff, Leonard. Objectivism: The Philosophy of Ayn Rand, chapter 10.

External links

Sex at the Ayn Rand Lexicon