Relative merits of AES ECB and CBC modes for securing data at rest
While I'll try to answer your question at a theoretical level below, I'd like to first stress the following:  It's a bad sign if, in the course of writing software, one is making such low-level decisions about encryption methods.  Encryption security is extremely brittle, with seemingly insignificant details causing complete failure.

With that said, the question brings up some interesting issues with encryption security versus efficiency.

As the other answer notes, ECB reveals when the same block has been enciphered twice and CBC does not (as long as the IV is unique or random).  If you are, for some reason, absolutely sure the same block will never be enciphered, then ECB is in theory fine.  (One technique might be to encipher the blocks in "batches" using a wide-input blockcipher, so that now a ciphertext will repeat only if an entire "batch" repeats.)  But in my opinion this is an unnecessary risk.

Will you ever change blocks of the data once it is written?  This need is one of the distinguishing requirements when dealing with "data at rest" (as opposed to e.g. data being sent over an SSL connection).  ECB, while insecure, will allow you to efficiently change the data in place while CBC will not.  But be aware that the security your are achieving in either case is not ideal.

In general, and especially if local updates are needed, a better technique is to employ a "tweakable block cipher" with the disk location as the tweak.  This will hide repeats amongst different blocks if one uses the block's index (disk location, etc) as the "tweak."  Moreover, it will allow for efficient updates.  This can be combined with the "batching" technique above to provide a level of security that seems pretty strong:  A repeat will only be noticed by an adversary who can watch you change the data, and only when you write the same batch of numbers to the same location twice.  Otherwise the data will be kept private in a strong sense.

It might be help to look at the IEEE 1619 standards documents and associated references for information about tweakable blockciphers and the wide-input batching technique.  The theory outlined there is a long way from a "secure" implementation, and again it seems you probably want to use an existing implementation of this stuff rather than roll own.