"You're a kind person. I don't think you'd be able to hate someone that much. If you were really that cold inside, I don't think I, or any of us, would like you." - Hitomi
"My heart wouldn't let me hide something from you. Because I love you." - Allen
In The Vision of Escaflowne, Hitomi Kanzaki develops a crush on Allen Schezar early on because he reminds her of her crush, Susumu Amano. Allen flirts with her but does not realize she has a crush on him. By the time he returns her feelings, Hitomi has already fallen in love with Van.
When the Mole Man tries to rob Hitomi of her pendant, Allen comes to her rescue. When Allen asks if she's all right, she mistakes him for Amano and faints from the tenseness of the situation. Likely because he resembles Amano, and because of his kindness and willingness to protect her (as opposed to Van's initial hard exterior), Hitomi develops a crush on him. Allen kisses her on the cheek, and makes other romantic passes at her, but remains oblivious of her crush.
At first, Allen treats Hitomi like a damsel in distress, believing that all the excitement has her delirious, and doesn't take any stock in her powers. However, when she does a tarot reading for him, discovering his resentment toward his father, and saves Van from danger on the Vione, Allen comes to respect her abilities.
After the group's arrival in Palas, Hitomi grows jealous when she sees Millerna's relationship with Allen, thinking that the two are lovers and that Allen is already taken. Though this isn't necessarily true, her belief that Allen is best for Millerna leads to conflicting feelings later about her developing relationship with Allen and Millerna's feelings for Dryden and for Allen.
Even before he develops feelings for her, Allen is very vulnerable around Hitomi. Early on, he tells her about his past, including Celena's disappearance and his mother's death, and in her reading she finds out about his father. Despite the difficulties in Allen's past, Hitomi respects him and looks up to him, and tells him she admires him and that she likes him.
During the journey to Atlantis, Allen leaves the room in frustration, caused by Dryden reading from his father's diary, and is conflicted over his hatred of his father for abandoning his family and his willingness to forgive his father. Hitomi goes after Allen and confronts him, claiming that he's not a cruel person and wouldn't be able to hold a grudge against someone. When the Crusade hits a levistone, they accidentally embrace, and Van, passing by, sees them and presumably assumes that this is a romantic gesture. Hitomi's willingness to forgive him, and her pulling him out of his conversation with his father when the group arrives in Atlantis, has a lasting effect on Allen and leads him to begin developing feelings for her. When Hitomi, Van, and Allen are transported to Zaibach, Allen is eager to protect Hitomi from the soldiers, and instead of letting her grab onto Van's hand to hop onto Escaflowne scoops her up in his arms and holds her tight during their ride out of Zaibach.
Sensing a possible connection between Hitomi and Allen, based on Hitomi's early crush on him and Allen's growing fondness for her, Emperor Dornkirk proposes using the Fate Alteration Machine to separate Van and Hitomi so that Escaflowne's power cannot be further awakened. On the eve of Millerna's wedding to Dryden, Allen and Hitomi are out walking in the rain and meet each other on a bridge. While being "mind controlled" by their equivalents Folken (for Allen) and Eriya (for Hitomi), Allen and Hitomi, the latter being somewhat reluctant, share a kiss. However, Van spotted them, and Hitomi feels conflicted about Van's disappointed and hurt reaction to their moment.
Allen shows very protective, even possessive, behavior toward Hitomi, telling her not to hide anything from him, and claiming that he may have to "lock [her] in a birdcage" if she keeps running off with Van. When she is kidnapped by Naria, Allen stands on bridge and wonders why everyone important to him is taken away from him. Before the final battle begins, Allen tells Hitomi that Chid is his illegitimate son by Marlene Aston. Hitomi is shocked by the revelation.
When Hitomi returns to Earth for the first time, Allen speaks to his father about Hitomi, telling him that he's happy that she returned to her home, even if he misses her. He comes to believe that he saw his sister Celena in her. When she returns to Gaea with Van, Allen has one last conversation with Hitomi, in which he accepts that her true love is Van, and encourages her to find him.