Yes. You can get coins from both chains if you do the right thing. To make sure you get it, there are two options:

1. Store your Bitcoin in your own address (you have control to the address private key). This method means you (and only you) are gaining full control of your Bitcoin. But to gain access to the forked coin process might be a little problem if you lack of technical knowledge. You have to install new wallet, import the address private key to the new wallet, and could only spend if the chain is stable. That means you couldn't sell your fork coin (B2X) immediately.

You can search on Google the detailed guide for claiming the fork coin. theymos, admin of Bitcointalk, also says he will make such guide later.

2. Store your Bitcoin on exchanges that support the fork. Exchanges that supports and will credit B2X to its user are: Bitfinex, HitBTC, Coinbase, GDAX. Full list here
If you're storing your Bitcoin on an exchange you didn't need to do anything to claim the fork coin and you can sell them immediately on that exchange. The downside is storing on an exchange isn't a good idea. You let them have control over your Bitcoin. They might not fulfill their promises or ran away with your money although that's highly unlikely.

I personally will store my Bitcoin on an exchange a moment before the fork because I want to sell the B2X immediately. I believe the original chain will maintain the status quo, i.e. having the most hash power, and keep its name (BTC).