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This is the chair mat I have.
Is it on a carpet or a hard floor? The plastic mats I used to use on carpet, had little nubs on the bottom side, to keep the matt in place. If on hardwood, maybe some strategically placed double sided tape? :)
 
Is it on a carpet or a hard floor? The plastic mats I used to use on carpet, had little nubs on the bottom side, to keep the matt in place. If on hardwood, maybe some strategically placed double sided tape? :)

Carpet
 
To add to Huntn's suggestions, you could also try a small rubber carpet pad that might provide some resistance.
 
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