Next step in progression from 3NF to BCNF
First, you assumption about the 3NF is correct.

Then, in the analysis algorithm to find the BNCF, when you start to remove a dependency X → Y since it violates the BCNF, you should put in the first relation H1 not only XY, but X+, while in the second relation you should have H2 = H - X+ + X.

So, in the first step, the two resulting relations are:

H1 = {A,B,C) with dependencies A → B and B → C and key `A`,
H2 = {A, D} (with no dependencies)


In H1 the dependency B → C violates the BCNF since B is not a superkey, and you can decompose it in:

H11 = {A, B} with the dependency A → B and key A
H12 = {B, C} with the dependency B → C and key B


So, at the end, the final decomposition is H11, H12 and H2. Note that this decomposition determines the loss of the dependency {C, D} → A, and this happens also if we start by considering first the dependency B → C (obtaining the same decomposition).