Fill a shaker with ice cubes. Add all ingredients. Stir and strain into a chilled cocktail glass. Garnish with lime.
One theory is that the drink was named after British Royal Navy Surgeon General Sir Thomas D. Gimlette, KCB (served 1879 to 1913), who allegedly introduced this drink as a means of inducing his messmates to take lime juice as an anti-scurvy medication. Limes and other citrus fruit have been used by the Royal Navy for the treatment of scurvy since the mid-18th century.