I agree with Pauline. In fact I keep my chives in a big bucket/Pots now on the allotment and bring one home to cut, then take it back and swap with another as I use them.
Every year, in spring, I cut them in half, and re-pot them. Giving away surplus.
So, you certainly are fine to dig up the patch and sort out the couch grass. Re plant in smaller clumps if you need to.
Mean while there is no reason not to grow a fresh lot in a small pot ready to replant. If you feel so inclined.