The blockchain is information. It is not a "thing," and it is copied wherever one wishes to have it.
Distributed systems like this are interesting, and it may help to think about a heretical phrasing: a blockchain. That's right. There is more than one.
A blockchain is any set of information (i.e. bytes) which describes a valid block chain. There are two ways to identify them:
- There is the original block, a block chain of length 1, which was defined to be a valid block chain in Satoshi's original publication. This is called the genesis block for any block chain system (This could be seen as a minimal level of centralization, but we usually don't pay much attention to it)
- Any sequence of blocks which meets the mathematical requirements of a block chain and starts with Satoshi's original block is a valid block chain.
So how do we get from a blockchain to the blockchain? Bitcoin defines the longest block chain to be "the" block chain at any given moment. More precisely, it is the most difficult block chain. Each block includes the answer to a math problem that requires a great deal of computational work, and the sum of that work is used to identify which block chain is the "longest."
Now bitcoin has been around long enough and enough CPU time has been burned on one chain that we can be extraordinarily confident that it is indeed the longest block chain in the bitcoin universe. We call this "the blockchain."
Sites like the blockchain explorers listed in RedGrittyBrick's answer will show you a block chain that they assert is the blockchain. And, due to the raw length of the chain, and the solid agreement between the explorers, we can be quite confident it is "the" block chain.
At least, we can be confident up to the last few blocks. There are many rules of thumb for how deep a block has to be before it is deemed truly irrevocable. I've heard the number 6 blocks thrown around. The idea behind this is that its possible for people to disagree about the tail of the block chain, just due to networking issues. There may be several valid block chains floating around the world at any point in time which are vying for the title "The Blockchain."
The bitcoin algorithm is designed to resolve this. The honest miners will pick which chain to add to, and will select one chain (this chain is selected both by the desire of the miners to keep the algorithm working, and from raw greed -- mining on a chain which ends up not being "the chain" was wasteful)
Once enough blocks have been mined, it becomes increasingly unlikely that anyone will ever contest which chain is longer, and the longest re-earns the title "the block chain."
So really, the blockchain is wherever someone wants it. It's public knowledge, and can be downloaded from many sites, or from the peer to peer network itself. You can verify that it is indeed a valid block chain. And, as Murch points out in his answer, you can choose to run a "fullnode" which is a node in the peer to peer network which regularly maintains the block chain to the best of its ability.