CPA on theoretical OTP with CBC mode
Scheme is not IND-CPA for any message longer than one block. I'll include a image of CBC mode below for reference (Source: Wikipedia).



Suppose instead of block cipher encryption we have plaintext xor-ed with the key as you propose. You'll note that for message block 1, $M_1$, the ciphertext block $C_1 = M_1 \oplus IV \oplus Key$. Similarly $C_2 = M_2 \oplus C_1 \oplus Key$ Substituting for $C_1$ we get $C_2 = M_2 \oplus M_1 \oplus IV \oplus Key \oplus Key$ which reduces to $C_2 = M_1 \oplus M_2 \oplus IV$. Knowing this we can build a distinguisher $D$. 

Suppose we send two messages $M0$ and $M1$ to the encryption oracle and get back $C$. $D$ will take $C$ and check if either $C_2 = M0_1 \oplus M0_2 \oplus IV$ or $C_2 = M1_1 \oplus M1_2 \oplus IV$ (note that the $IV$ is not secret), returning whichever plaintext corresponds to $C$. Clearly this distinguisher has non-negligible advantage, and thus the scheme is not IND-CPA for messages longer than one block.