The main conflict in “The Story of an Hour” is that between Louise Mallard, the protagonist, and her society. The story was written in the 1890s, and context clues would suggest that it takes place during this same era. In the 1890s, women in the United States had few rights. When they married, their identities became, in a manner of speaking, legally covered by their husbands’ identities, and any property they owned prior to the marriage became their husbands’. Women could not legally vote, as it was assumed that a woman had no need to vote because either her father or her husband would vote for the household.

Despite this, it is not Brently Mallard, Louise’s reportedly dead husband, who poses as her antagonist throughout the story. When Louise reflects on his life, she thinks of his “kind, tender hands” and how he “never looked save with love upon her.” This means that he only ever looked at her with love. Instead, it seems to be the restrictions and the repression of her individual identity imposed by the marriage state that upset Louise so much. Brently’s legal right to make decisions for her—and her lack of legal rights to act independently of him, no matter how loving he was—antagonize her. This is what makes society the antagonist in this story and the conflict between Louise Mallard and her society the main conflict.

I would say this story serves as an example of person vs. society (though in this context, one might also see elements of person vs. self).

"The Story of an Hour" opens with Louise Mallard being alerted to the news of her husband's death (news that will be shown to be false at the end of story). After hearing this news, she falls into grief and retreats into her room. As the story continues, it follows the evolution of Louise Mallard's emotions in the aftermath of this moment. In this, it certainly contains a strong element of person vs. self (and should be viewed in such a lens).

At the same time, however, this story ultimately centers around an epiphany on Mrs. Mallard's part that stems from a far deeper struggle against the society in which she resides. It is this epiphany that ultimately empowers her, giving rise to what Kate Chopin refers to, within the story itself, as "a monstrous joy." Ultimately, widowhood means the realization of personal agency. For the first time, Louise Mallard belongs to herself.

Thus, her husband's death has set her free. Note, however, that she does not seem to harbor any particular resentment to her husband himself. Indeed, consider how Kate Chopin writes the following about him:

She knew that she would weep again when she saw the kind, tender hands folded in death; the face that had never looked save with love upon her, fixed and gray and dead.

This, then, is not a story shaped by person vs. person conflict. Rather, her problem is the sexist and chauvinistic foundations that lie within the society she inhabits. It is these assumptions and expectations that she is struggling to overcome.

The fundamental conflict in Chopin's work is the idea of what is supposed to be experienced as opposed to what is experienced.  Louise finds herself poised between these incommensurate ends when she is told of her husband's death.  The socially conditioned response is for her to mourn his passing, but the personal response which responds the essence of her conflict is the newly discovered freedom and sense of self that is now upon her.  This becomes a critical conflict within Louise.  While experiencing the loss of her husband provides one set of responses, the new definition of self which awaits gives her another set of responses.  This conflict between what social conditioning and personal experience represents a fundamental battle within Louise.

I agree with the previous poster. The conflict in Kate Chopin's short story "The Story of an Hour" is entirely expressed through the thoughts of Mrs. Mallard -- the report of her husband's death makes her, perhaps for the first time, understand how she has been feeling all this time. That self-awareness -- that thing "too subtle and elusive to name" -- is achieved when she utters the words "free, free, free!" That Mrs. Mallard has indeed been dominated by men, as the previous poster, and by the rigid social conventions for women of her class at the turn of the century can be seen in how she is treated in the story. Her husband's friend is the first to hear and deliver the news of the accident and the one who tries to "screen" the husband from the wife's view. Her sister is the one who breaks the news to her and pleads to be allowed into her locked room. Everyone seems to act on her; she does almost nothing physical, on her own, in the story.

To me, the conflict in this story is between Mrs. Louise Mallard and the society in which she lives.  Her desire to be an independent woman is in conflict with the society she lives in, which is dominated by men.

In the story, Mrs. Mallard finds out her husband is (supposedly) dead.  She discovers, as she thinks about it, that she really is happy that he is dead.  Now she will be able to do what she wants to do rather than having to go along with his desires.  When she finds out he is really alive, she dies of a heart attack.

So, she really wants to be independent, but her society will never let her be while she and her husband are both alive.