Your thesis statement should directly address a question or discussion point and summarize your whole argument. Often, it is easier to write the thesis statement after you have created most of your essay or speech; so remember that even if you come up with the perfect thesis statement, you might want to go back and change it later. That’s fine, and it shows that you are learning about the subject.

If we think about the discussion point here as being “the irony of Armand’s heritage,” we can begin to unpack what that means and try to respond to it. The irony here comes from the tragedy of Desiree’s death as a result of Armand’s racist cruelty toward her. It is not quite clear whether Armand is aware of his heritage all along; his mother, who was a Frenchwoman, died when he was six years old. It could be that upon seeing his son, Armand realized that he himself was black, or that he knew all along but kept it hidden, or that he truly did not know until he was finally clearing out his desk after Desiree committed suicide and found the letter from his mother to his father. We do know, though, that by the end of the story, Armand knows that his mother was black and wants to destroy evidence of this fact.

The irony comes from the contrast between how Armand behaves in the world and how he thinks of himself. Armand is unspeakably cruel to black people: he owns slaves, whom he beats, and he sends his wife away when he thinks she is black (and so, by extension, is their son, whom he previously loved). To structure a thesis statement about this topic, you could use the noun phrase “Armand’s heritage” as the subject, and then decide on what the revelation of his heritage tells you about the theme. For example,

Armand’s heritage is revealed as a plot twist at the end of the story to illustrate the absurdity of the idea of racial purity.

A thesis statement should make a claim that can be supported using textual evidence from the text it addresses. You might, therefore, argue that Chopin foreshadows the eventual questions surrounding Désirée's racial heritage when she writes that Désirée was found in shadow, again referencing that shadow when Armand Aubigny first sees and falls in love with her and when Monsieur Valmonde reminds Aubigny of Désirée's unknown origin.

The narrator reports that Désirée was found by Monsieur Valmonde "lying asleep in the shadow of the big stone pillar" in front of the plantation. This shadow would have the effect of temporarily making her skin seem darker, as we all appear darker in shadow; the repeated reference to and apparent symbolism of this shadow makes it seem as though Désirée might, in fact, have black ancestry (referring both to the physical "darkness" of blackness and to the truth of her heritage, which is kept the dark).

Furthermore, even Désirée's adopted father urges Aubigny to have caution as a result of Désirée's "obscure origin," but Aubigny's feelings are described as though he'd been "struck by a pistol shot"or as being like "an avalanche, or like a prairie fire"—all things that are dangerous and damaging; this too provides some foreshadowing of Désirée's catastrophic tragedy when she is cast out as abruptly as she was taken in.

You might also argue that the descriptions of the slaves' skin tones, as well as clues regarding Désirée's baby's, provides evidence for just how concerned people were with how much white or black parentage one had (including what we learn to be Armand's own). Désirée is wearing "soft white muslins" which contrast with the "yellow nurse woman," Zandrine. Désirée reports that Armand could hear the child crying from "'as far away as La Blanche's cabin": La Blanche seems to be a nickname for a slave whose skin is nearly white. The narrator reports "an air of mystery among the blacks," and that one of La Blanche's little "quadroon boys" fans the child. These nicknames and words like "quadroon" (which mean that a person has one black grandparent—is one-quarter black) show the preoccupation with race and heritage.

Furthermore, if La Blanche has "quadroon boys," then that must mean that she is what was called a mulatto (with one black parent and one white parent), and the boys' father must be supposed to be white; if we connect the dots, we might even come to the conclusion that Armand is the boys' father: what other white man would be having sex with Aubigny's slaves? How ironic and fundamentally hypocritical that he is not only part black but also that he would cast his wife out for being partially black—all the while continuously raping slaves.

In writing about the racial undertones that dictate concerns on the part of Desiree's parents as well as on the part of her husband, Armand, you may wish to compose a thesis that sets up a comparison/contrast.  For, the reaction that Madame Valmonde has to the prospect of Desiree not being white is certainly not the same as the reaction of Desiree's husband, Armaud.

Thus, there is a statement about the nature of love.  Madame Valmonde does not waiver in her maternal love for Desiree, the baby that she believed "a beneficent Providence had sent her.  For, when Desiree writes to her, she does not confirm or deny anything; she simply tells Desiree to come home.  On the other hand, Armaud who "fell in love as if struck by a pistol shot," rejects both his wife and baby.  He coldly tells Desiree he wants her to go.  Without proof of anything, he rejects her:

...he no longer loved her, because of the unconscious injury she had brought upon his home and his name.

Ironically, it is only after Desiree has gone that Armaud learns the truth.

Are you writing on both topics, or do you have to choose one? If you are discussing the broader subject of racial undertones, your thesis sentence should suggest something about race in the story and should specifically identify some examples of racial undertones. For example:

The rife racial undertones in Chopin's "Desiree's Baby" govern the characters, causing Desiree's adopted parents to worry about her ethnic background, enabling Armand to treat "his" slaves with cruelty, and granting him the power to disown his wife and child.

If you are writing about the narrower topic of irony or the irony of Armand's heritage, your thesis statement should discuss Chopin's use of foreshadowing (which certainly includes the racial undertones) to lead logically to the story's ironic ending.