President Arthur was a widower when he entered the White House unexpectadly in 1881. His wife "Nell" (Ellen Lewis Herndon Arthur) had died of pneumonia on January 12, 1880. Her White House biography notes Chester Arthur's grief, "That November, when he was elected Vice President, he was still mourning her bitterly. In his own words: 'Honors to me now are not what they once were.' His grief was the more poignant because she was only 42 and her death sudden. Just two days earlier she had attended a benefit concert in New York City--while he was busy with politics in Albany--and she caught cold that night while waiting for her carriage. She was already unconscious when he reached her side."
Despite his grief, President Arthur still was known to notice ladies. One that has gone down in history is one President Arthur probably wishes history had not known about, Victoria Sackville. She was the illegitimate daughter of the Lionel Sackville-West, 2nd Baron Sackville and the Spanish dancer Josefa de la Oliva (née Durán y Ortega, known as Pepita). She later married her third cousin and became Victoria Sackville-West, Baroness Sackville.
At 19, Victoria went to Washington to serve as her father's hostess at the British-Legation. She was very popular and many men fell in love with her. Chester Arthur was one of them. According to Barbara Holland in Hail to the Chiefs (2003), Victoria claimed that President Arthur proposed to her. She wrote later the she "burst out laughing and said, 'Mr. President, you have a son older than me and you are as old as my father." Properly chastised, President Arthur dropped the matter.
Arthur would only survive his presidency by two years. It would have been a short marriage anyway. Victoria Sackville-West is best remembered today for her daughter Vita Sackville-West. Wikipedia notes, "Her life is mostly overshadowed by the high-profile and controversial lesbian lifestyle of her daughter, Vita, whose up and down and often volatile relationship with Violet Trefusis was the subject of gossip for several years."