Connie Boswell - The Nearness Of You (H. Carmichael), 1940

From Wikipedia:
Constance Boswell (December 3, 1907 - October 11, 1976) was an American female vocalist born in Kansas City, Missouri but raised in New Orleans, Louisiana. With her sisters, Martha and Helvetia "Vet" Boswell, she performed in the 1930's as The Boswell Sisters and became a highly influential singing group during this period via recordings and radio. Connee (or Connie) herself is widely considered one of the greatest jazz female vocalists and was a major influence on Ella Fitzgerald.
In 1936, all the sisters got married, and Vet and Martha retired. Connie, on the other hand, even though she cut solo albums while with the group, directed her entire focus on her solo career. This collection represents some of her guest appearances in various old time radio shows including Bing Crosby, Command Performance, Good News, Kraft Music Hall, Mail Call, and Screen Guild Theater.
"The Nearness Of You" was originally written by Ned Jones and Hoagy Carmichael for the movie "Romance In The Dark" (1937) with Gladys Swarthout and John Boles.
Recording: Connie Boswell -- The Nearness Of You (H.Carmichael), Decca 1940