An Introduction includes the orientation of the story in the broader field of literature as well as your purpose and aim in addressing your particular idea (thesis) about the topic. While some advocate a "grabber" introduction, I find that solid, thoughtful information presented in a succinct manner is more interesting than a clever "hook" in academic writing.
Sometimes a good way to generate a thesis or introduction is to look at what others have had to say about a work. One way to get a quick sense of previous discussions is to consult a survey of previous analyses. Since I'm the author of such a survey (Kate Chopin's Short Fiction: A Critical Companion), I've appended below just the very beginning of the survey of criticism on "The Story of an Hour." You may find something here that is helpful to you as a point of departure -- something with which you can either agree, disagree, or develop further. If your library doesn't have the book, you can get a copy through interlibrary loan to get the full citations. Good luck!
Rankin 1932: Chopin’s own father had died in a train accident. Chopin minutely altered the originally published version of the present story (34). Arms 1967: Although this relatively successful work has been called one of the best stories from Chopin’s last collection, its irony seems a bit contrived (225). Seyersted 1969a: This genuinely noteworthy and surprising tale suggests how the success of Chopin’s first published collection of stories had increased her self-confidence, artistic liberty and literary daring; she composed the tale -- with its unusually blunt emphasis on feminine independence -- just when the positive reviews of Bayou Folk had begun appearing (57-58). Ironically, the tale was rejected for publication by the first (male) editor to whom she submitted it. He probably considered it immoral (68), and it was certainly her most shocking depiction so far of a woman’s desire for autonomy (111). She produced it during a year when she felt she had become more mature as a writer (123), yet serious critical interest in the story did not really begin until 1961 (189). The tale was translated into French by one of Chopin’s contemporaries (although the translation apparently was never published ), and despite the fact that it was initially turned down for publication by the second journal to which she submitted it, the journal did later publish the story, seemingly unaltered, after positive reviews of Bayou Folk appeared (209). This tale is one of several that Chopin wrote in pairs, with one work emphasizing feminine self-assertion and the other work (in this case a journal entry) emphasizing feminine compliance (216). Seyersted 1969b: Chopin was prompted to write this work as a result of the favorable notoriety she had achieved with her first collection of stories; perhaps the story implies her sense of having been constrained in her own marriage. In any case, she now felt greater self-assurance. Even so, this story was rejected by an editor, probably on moral grounds (25). Leary 1970a: This extremely brief tale is nonetheless rich in shifts of plot and theme (xi-xii). Leary 1970b: This is one of Chopin’s best tales (140-41). Leary 1971: With its rapid oscillations and brevity, this tale treats more openly than some of Chopin’s local-color fiction the theme of feminine independence (168). Peterson 1972: Here as in some of her other best works, Chopin avoids general moralizing by keeping her focus on one specific case (123-24). The twist at the conclusion emphasizes the idea of alienation. The conclusion is a bit forced, but the need for independence is made obvious (137-39). In this work Chopin for the first time openly confronts the problems of marriage (142). The story illustrates her tendency during this period to treat unusual topics in an objective tone (161). Rocks 1972: Here as elsewhere Chopin shows that a loveless or oppressive marriage is unethical (119). Bender 1974: As in many of Chopin’s tales, emotions associated with liberation are linked here with imagery of nature. The original title of the story (“The Dream of an Hour”) also associated such emotions with the unconscious (264-65). Seyersted 1974: A month after writing this story, Chopin herself lamented her own widowhood (13). This was one of a number of the more adventurous works Chopin began to compose as her fiction began to achieve success (14). Arner 1975: Like Edna in The Awakening, Mrs. Mallard can achieve liberty only by dying (88). Skaggs 1975: This story shows Chopin’s progress in exploring the victimhood resulting from males’ sense owning women (285).
Kate Chopin's "The Story of an Hour" has its greater meaning impingent upon the social context of what she writes. So, to underscore #3 and #4, an introduction that presents the Victorian law of patriarchal proprietary rights is essential. Also, some emphasis upon the concept of repression may give direction to an essay, paper, etc. For, this is what Chopin means by her metaphors about "a heart trouble" and "a joy that kills."
I think I agree with #3. Obviously, your introduction will be shaped by your essay, but your introduction would have to do something to bring alive the social situation that women faced at the time the story was written to be able to explore how the author uses this story as a kind of protest against this state.
A good introduction to The Story of an Hour would be stating that the social expectations placed on women less than two centuries ago denote a tendency of placing womanhood in front of femininity, that is, to underrate the needs of women in favor of their physical capacities of bearing children and supporting a family. Mrs. Mallard's "heart trouble" may very well be the result of a life in which she had consistently buried her own wants and needs in order to fulfill the expectations society had bestowed upon her as a woman. When her heart was finally "set free" upon learning of the death of her husband, she tasted the flavor of her own life and the possibility of gaining herself back. When she found out this was all a mistake, that same "bad heart" which was set free refused to go back to where it was. Therefore, she died supposedly "of joy" of finding out her husband was alive after all.
I think that the introduction to whatever you are writing has to be reflective of this content. It is for this reason why I think that more information is going to have to be given. The initial line of discussion here would be what is your thesis statement, or what is going to be proven in your paper. Once this is answered, I believe that being able to deliver an introduction can be properly formulated. Certainly, a part of your introduction could involve how Chopin enjoys to explore the aspect of womanhood that might not be fully embraced by society. In her works, she explores a more autonomous and defiant role of what it means to be a woman, and this is on display with Louise's character in the short story. However, more relevant insight into an introduction can only really come out of a more specific discussion of what the topic of the paper is and what is being proven within it.