A coonskin cap
A coonskin cap is an Earth garment made from the hide of a raccoon. It was popularized by Davy Crockett.
After their experiences at AR-558, Ezri observed that Bashir and O'Brien spent even more time than before in the holosuite playing their Battle of the Alamo simulation. She half-expected O'Brien to come to work in a coonskin cap. (DS9: "It's Only a Paper Moon")
Vic Fontaine was given a coonskin cap to wear when Bashir and O'Brien tried to get him to join their simulation. He claimed he didn't look good in buckskin (referring to the period clothing that accompanied the Alamo), but later changed his mind and said he'd see them there, "coonskin cap and all." (DS9: "Badda-Bing, Badda-Bang")
Bashir jokingly claimed that O'Brien was "very sensitive" about who saw him in a coonskin cap. (DS9: "Field of Fire")