Chak is not entirely correct. The exchange is the matching engine, but there will be someone else on the other side of the trade. The exchange does not have its own position in futures.
That said, legally each party to the future has the exchange as the counterparty (i.e. there are two separate contracts). This all but eliminates counterparty risk. Compare this with a forward, which is effectively a future struck direct between two parties, with no exchange.
Most exchanges have what are called market makers, which in return for being spared some or all exchange fees, commit to providing a buy and sell price for all (or a high proportion) of the time the exchange is running. So most people in practice are trading with a market maker who is bearing the risk of being on the wrong end of the trade. But you could be trading with anyone, either an individual or an institution who wants the opposite exposure to you.
Update As Max Vernon says, the Bitcoin futures on CBOE are cash-settled, not physically-settled. Physically-settled would be a poor choice for Bitcoin, because there could end up a situation where not all futures can be settled given the liquidity available. And as the price rocketed as (some) futures sellers had to buy bitcoin, everyone else would hang on to it.