To see the problem, let's see how I would chain up a single function (call it $AES\,CBC_k(iv, m)$) which only encrypts a single block at a time into something that can encrypt "chunks" of any size.
Let $m=m_1||m_2||m_3||m_4$ be the message I want to encrypt. Each $m_i$ is a single block (in AES it is 128 bits). I want to use $AES\,CBC_k$ to encrypt $m$. The proper way to do this would be to compute:
Then let $c=c_1||c_2||c_3||c_4$ be the ciphertext. Using this process (note how the iv changes from block to block), we could build another function, say $E_k$ which encrypts messages of any length (actually a multiple of the block size).
To illustrate your problem, let's split $m$ into two chunks: $m_1||m_2$ and $m_3||m_4$ and see what it sounds like you are doing. It sounds like you are calling $E_k(iv, m_1||m_2)$ then $E_k(iv, m_3||m_4)$. This is like doing the following.
Notice the iv for $c_3$ and compare it with the iv for $c_3$ in the correct operation above.
So, if you really want to encrypt the way you are talking about doing, you would need to use the last block of the previous chunk as the iv for the next chunk. Managing this yourself in code, while do able, is somewhat of a pain. I'm willing to bet there is an encryption library for PHP that can so this for you (on file streams or something so the whole file doesn't have to be in memory).
The real question
So it sounds like your real question is how to encrypt large files in php without having to read the whole thing in to memory. I don't use PHP much, so I can't really comment. I will say don't use the solution here as it was obviously not designed by anyone who knows anything about cryptography. I know in other languages (Java, c#) you can pass in a file stream to be encrypted in most libraries, which probably solves the problem of having to read in all the memory. Not sure if PHP has something like that though.
It looks like php has encryption filters that you could use with stream_filter_append to encrypt streams so that the file doesn't have to be loaded into memory. Then you would have a stream to read from and a stream to write to. Simply read from the input stream and write to the output stream. The encryption happens automatically thanks to the filter.