Now the BCC miners are actually working on producing the first BCC-only block, which will be block 478559 on the BCC chain and will be different from block 478559 on the BTC chain, hence effectively splitting the chain.
Since BCC has only a tiny fraction of BTC's hash rate (around 1% by most estimates, although it's pretty hard to evaluate) it will take a while for this block to be found. Probably hours, maybe even days.
Eventually the difficulty on the BCC chain will adjust, so even if the hash rate remains low the "blockrate" should steadily increase within the next few weeks. Also since BCC blocks can be 8 times as big they can fit more transactions in a single block, somewhat mitigating the effect.