If Andy Hall's team win, they will play Buckinghamshire or Wiltshire in the third round on Sunday, July 10.
Cheshire have also had provisional dates confirmed for their six matches in the Minor Counties Championship Western Division for next season.
Hall's side travel to Herefordshire in their opening match between June 5-7, followed by clashes with Cornwall, Devon, Wiltshire, Oxfordshire and Wales.
Fixtures: Herefordshire (away, June 5-7), Cornwall (home, June 19-21), Devon (away, 3-5 July), Wiltshire (away July 17-19), Oxfordshire (home, August 7-9) and Wales (home, August 21-23). Tweet

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