Sempervivum (Hens & Chicks), like some Agave and Tillandsia (Air Plants), are monocarpic, meaning that each plant can only bloom once in its lifetime. Fortunately, a Semp rosette will grow for many years and produce lots offsets (chicks) before blooming out, and the chicks will live on.
You can temporarily halt the blooming process by scooping out the bloom stalk with a sharp, clean knife. This only works if you catch the bloom stalk as soon as the rosette center starts to close in and elongate. Cutting out blooms will not prevent flowering indefinitely or return you to the single, perfectly symmetrical mother hen you started with, but it can give you more offsets to transplant before the original rosette eventually dies.
For more information on Sempervivum flowers, what triggers blooms, and how to temporarily prevent them, check out the full Visual Guide to Sempervivum Blooms.