The draw was made live on Facebook by Ray Wilkins.
The Spireites will travel to Rochdale in the first week of the season.
Last season Chesterfield were beaten 2-1 in the JP Trophy by Rochdale.
But in league action the Spireites won at Spotland and drew 0-0 at the Proact.
Round two will be played on the week commencing 21st August.