I started my Chive plants from seeds two years back. Just a few seeds germinated but over the years the tiny bulbs multiplied leaving the older plants with long and unpleasant base. It is time to re-pot.
You can do the same with your Chives and other herbs by carefully lifting the plants without disturbing the roots . Use a fork if they don't come out easily. In Karachi, its best to do this during spring, monsoon or during very early winters.
Keep your new pot ready with some new soil mix. Transfer the Chives with long and unpleasant base a bit deeper than before. Cover with more soil and water softly. You Chives will look good as new.
Now I have one pot of 2 years old Chives and the one of young Chives that are keeping away pests from my Rose vine.
I hope this helped you in some way.