Taken from Billboard (thanks to Norm Perry)

March 28, 1942

 1   1   7   MOONLIGHT COCKTAIL - Glenn Miller & His Orch. w. vocal/Ray Eberle & The Modernaires
 2   2   6   I DON'T WANT TO WALK WITHOUT YOU - Harry James & His Music Makers w. vocal/Helen Forrest
 3   3  12  *A STRING OF PEARLS - Glenn Miller & His Orch.
 4   4   5   DEEP IN THE HEART OF TEXAS - Bing Crosby w. Woody Herman & His Orch.
 5   5   5   BLUES IN THE NIGHT - Dinah Shore
 6  --  NEW  DEEP IN THE HEART OF TEXAS - Alvino Rey & His Orch. w. vocal/Bill Schallen & Skeets Herfurt
 7  --  NEW  JERSEY BOUNCE - Benny Goodman & His Orch.
 8   6   2   SOMEBODY ELSE IS TAKING MY PLACE - Benny Goodman & His Orch. w. vocal/Peggy Lee
 9  --  NEW  I DON'T WANT TO WALK WITHOUT YOU - Bing Crosby
10  --  NEW  SOMEBODY ELSE IS TAKING MY PLACE - Russ Morgan & His Orch. w. vocal/The Morganaires