Yes, it is common for a new motorcycle chain to experience some initial stretching during its break-in period. The stretching of a new chain is typically due to the settling of the chain's components and the adjustment of the links as they mesh with the sprockets.
During the break-in period, it is important to regularly check and adjust the tension of the chain to ensure proper functionality and to minimize wear on the sprockets. Most motorcycle manufacturers provide guidelines on how to adjust the chain tension and recommend specific maintenance intervals.
After the initial break-in period, the chain should stabilize, and the stretching should be minimal. However, it's worth noting that all chains gradually wear over time and will require periodic adjustment and eventual replacement. Regular maintenance, including lubrication and proper tensioning, can help prolong the life of the chain and sprockets.