This promotional postcard was sent to listeners of NBC Radio's Chesterfield Supper Club in 1945 and can be dated by the card's postmark. There are no copyright marks on either side, as can be seen in the photo links. It is well within the free license timeframe.
It was created for distribution to the radio show's listeners to induce regular listening and also to promote the Chesterfield brand of cigarettes.
This card pre-dates the co-hosting of the program by Jo Stafford (did not begin until 1946) and Peggy Lee (did not begin until 1948).
United States Copyright Office page 2 "Visually Perceptible Copies The notice for visually perceptible copies should contain all three elements described below. They should appear together or in close proximity on the copies.
2 The year of first publication. If the work is a derivative work or a compilation incorporating previously published material, the year date of first publication of the derivative work or compilation is sufficient. Examples of derivative works are translations or dramatizations; an example of a compilation is an anthology. The year may be omitted when a pictorial, graphic, or sculptural work, with accompanying textual matter, if any, is reproduced in or on greeting cards, postcards, stationery, jewelry, dolls, toys, or useful articles.
Note that it may still be copyrighted in jurisdictions that do not apply the rule of the shorter term for US works (depending on the date of the author's death), such as Canada (50 p.m.a.), Mainland China (50 p.m.a., not Hong Kong or Macao), Germany (70 p.m.a.), Mexico (100 p.m.a.), Switzerland (70 p.m.a.), and other countries with individual treaties.