Even though they only take 4 -6 weeks to mature, it is advisable that you not harvest any leaves for the first 1.5 - 2 months, even though the plant appears mature. They should be about 6" or taller. The plant needs to build up its root systems energy to support future harvests. Chives can be productive for several years even with repeated harvests, but they need to establish themselves first.
Keeping this in mind you are aware that it will take up a significant amount of time during which that bed could be utilized for other purposes.
As part of you routine maintenance, larger root clumps should be divided and cut back every few months to keep excessive root development in check.
Keeping excessive root growth in check will lead to a healthier plant and more abundant harvest it will also help to prevent nutrient ponding. Nutrient ponding is the accumulation of nutrient and solution in gullies and conduits created by uneven flow of liquid. Large root masses that are sometimes common with unkempt root systems can contribute to this.
Large unruly root masses also promote fungal growth, fungal growth starves the system of oxygen and attracts fungus gnats and on and on. See - Algae Buildup in Hydroponics
Another maintenance chore necessary when growing chives, whether in a conventional garden or a hydroponic garden is trimming flowers. Chive plants exist to reproduce via flowering and will diligently work at this task. You need to be just as diligent in preventing this. Removing flowers as they bud will force the plants energy to go into producing foliage and leaves instead of flowers. A few flowers here and there aren't harmful - but remove about 90% of them.
The foliage quality of chives that do not experience a dormant period diminishes somewhat, you would also if you worked 24/7 year round with no sleep. The life expectancy of plants that are continuously cropped also diminishes so it is advisable that plants be replaced roughly every 2 years.
Chives will grow continuously so long as the conditions are favorable. Temperature, humidity and light. In nature their cue to go into dormancy is the shift in temperatures and the lower light levels that winter yields.
In a controlled environment - such as most hydroponic setups 12 hours minimum, but 14 hours of daily light is best.
Standard fluorescent lamps will suffice. High output fluorescent grow lights or compact fluorescent lights are better. High intensity discharge lights are a step up, as are LED Grow Lights. LEDs are cost effective, they use much less electricity than any other light source. Their longevity is also unparalleled, rated at about 50,000 hours, although some manufacturers are claiming 100,000 for newer versions. See - Grow Lights
Airflow - Keep an oscillating fan running gently a few hours daily to stimulate sturdier plant growth and facilitate transpiration.
Temperature and Humidity
Chives grow and produce best at air temperatures of 65 - 70 F.Temperatures below Below 50°F, growth is sluggish and dormancy is induced. Above 80°F and foliage growth is impaired, flower production increases.
Nutrient Solution temperature is slightly different See: Hydroponic Temperature
Basically - a standard vegetative nutrient formula will work just fine. BUT sulfur and nitrogen should be added in moderation, periodically for increased flavor, quality and production.
Chives are Alliums, all alliums do well with a pH of at least 6.0, up to 6.5. As always, you should follow the guidelines of the nutrient line that you are using to ensure that your plants are receiving the proper quantities of macro and micro-nutrients.
Sulfur - elevated levels of sulfur promotes the production of the aromatic essential oils essential for the best quality.
Nitrogen - Nitrogen is also essential, but in moderation. Nitrogen promotes the growth of foliage but excessive nitrogen will produce a lush and poor quality foliage, sometimes unpalatable. Too little Nitrogen will bring about less harvestable foliage and a lower leaf quality. It can also accelerate the ageing of the plant and severely reduce its life expectancy.
Stressing the plants for short periods with low moisture levels or an elevated EC can concentrate flavor compounds, but may also induce bolting. This is best done for very short intervals just prior to Harvest.
Once your plants have matured satisfactorily, a small amount can be harvested. Use a sharp utensil, sharp shears or scissors in order to minimize cellular damage to the plant. You want it to regenerate and produce more harvests. You should expect to see very little browning post harvest if it is done carefully.
Be like a surgeon and treat your plant like a virgin, cut for the very first time. Leaves should be gently and surgically cut about 2 " above the plant base.
Eventually the plants, after many harvests, can become less productive, so replacing plants every two years with new seedlings or divisions is a good idea.