Neither keeper had a save to make in yet another stalemate on the road for the Coasters.
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Fylde remain unbeaten in eight away games in the National League this season, though seven have been drawn, including five 0-0s.
Dave Challinor's side have scored and conceded only once in four matches on their travels and there was little goalmouth action to excite the Proact crowd.
Fylde made one change to their starting line-up, with Tom Brewitt replacing Serhat Tasdemir, while winger Danny Williams was named among the substitutes a day after completing his loan move from Accrington Stanley.
Kick-off was preceded by a minute's silence in memory of Karole Woodthorpe, wife of Coasters assistant manager, Colin. The players wore black armbands.
The first goalmouth action came on eight minutes, when Danny Rowe's cross/shot whistled wide of the far post.
Both sides tried to play passing football but the keepers were not called into action, Marc-Antoine Fortune volleying over for the hosts on 24 minutes and Will Evans blasting a free-kick too high three minutes later.
Chesterfield were without a win in 11 matches, having won their opening three following relegation from the Football League, and they began to apply pressure.
The hosts went closer six minutes before the break, when Jerome Binnom-Williams' free-kick was headed wide by Curtis Weston at the back post.
Having mostly passed the ball around with little penetration, Fylde created the best chance of the half just before the interval, when Rowe's cross from the right reached an unmarked Joe Cardle, who should have hit the target from six yards.
If chances had been at a premium in the first half, there were even fewer in the second.
A clash of heads between Rowe and Evans, which left both players in need of treatment, was the only incident of note until the 71st minute, when a good passing move saw Danny Philliskirk release Rowe, who chipped over.
Debutant Williams came on for the closing stages but it was fellow substitute Ash Hemmings who had the final chance six minutes from the end, heading wide of the right post.
The major talking point came a minute later, when referee Joe Hull brandished a red card for a deliberate Chesterfield handball but reversed his decision.
Fylde remain seventh in the table and Chesterfield just one place above the bottom four.
Fylde: Lynch, Birch, Byrne, Tunnicliffe, Francis-Angol, Brewitt (Williams 79), Croasdale, Kellermann, Philliskirk, Cardle (Hemmings 72), Rowe; subs not used: Kane, Bond, Tasdemir
Chesterfield: Burton, Maguire, Evans, Rowley, Binnom-Williams (Reid 80), Muggleton, Weston, Smith, Fortune (Amantchi 65), Shaw, Denton; not used: Ofoegbu, Hollis, Kayode
Referee: Joe Hull