Starting Chives from seed is the most common method of beginning a chive patch.
Sow chive seeds about 1/2 inch deep in starter tray, peat pots or other suitable containers. Keep the potting mix consistently moist, but not soggy. Optimal temperature range for germination is 60-70 degrees F. It's not really a good idea to add any fertilizer when planting seeds, all the nutrients needed for germination are already within the seed itself. Fertilizer especially excessive fertilizer has the potential to cause more harm than good.
The seeds should germinate and begin popping out of the soil in 2 to 3 weeks. Give them another 1 to 2 weeks before transplanting them outdoors. When transplanting always wait till after the last possible frost date in your region, you should also harden off the seedlings for a day or two before committing them to the outdoor environment. See: Hardening Off Seedlings
Chive seeds can be planted outdoors if you would like to circumvent the transplant process. Planting of outdoors seeds should commence 4 - 6 weeks before the last anticipated frost date in your region. They are somewhat cold hardy but can die back if planted too early so it is best to wait until the soil has warmed sufficiently, soil temperature should be above 60 F.