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.
