IVs are not really meant to be secret, IIRC. They're just meant to be different each time, to avoid getting the same cypher text if you have to encrypt another plaintext that begins with the same block.
To clarify, not that this should ever matter for you because you should never work with these primitives directly, but a CBC IV needs not only to be unique but also unpredictable (which is a different property than "secret", of course).
This would be used in a chosen plaintext attack, right? If you saw a ciphertext C1 with IV1, and you were able to choose the following Pj and predict the corresponding IVj, then you could verify whether the plaintext of C1 was P1~ by choosing Pj = P1~ XOR IV1 XOR IVj, so that Cj = C1 iff Pj = P1~. This would allow you to test likely values of P1~ from a dictionary.
