How can I break a filter down into second order sections?
Below the results as sos matrix and gain. Every row in the matrix is a single second order section in the coefficient order of b0, b1, b2, a0, a1, a2. Obviously we need a0=1, and the sections are normalized so that b0=1 as well. The overall gain accumulated is in the single number "gain". The fact that this gain is actually in the order of 10^-9 shows that this is a numerically tricky beast.

Here is how this works.


Design the filter in poles and zeros (zp or zpk), NOT in polynomial form (ba). I imagine that the cheby1() function has an output option for that. If not, you can't use it.
The poles come in conjugate complex pairs, the zeros in this case are real, but you can think of them as a conjugate complex pair with a phase of 0.
Group one pole pair each with one zero pair. Start with the pole pair that has the highest magnitude and find that zero pair that's closest to it. This step is really important!!
Turn the poles and zeros into polynomial in 1/z of the shape (1-p/z)*(1-p'/z). Let's say the complex zero/pole is x+j*y. Then b0/a0 coefficients are always 1, the b1/a1 coefficients are -2*x and the b2/a2 coefficients are x^2+y^2.
Repeat over all poles. Each conjugate pole pair results in one second order section.


A word of caution, if I may: If none of things that I have listed above mean anything to you, than you probably should not be doing this. This is not trivial and many things can go wrong in non-obvious ways. Depending on what you are planning to do with the results, you really want to make sure that your code is fully vetted and properly tested. Unless you have a good idea on how to test this, I would not base anything mission critical on the results.


    sos =
   1.000000000000000   2.000000000000000   1.000000000000000   1.000000000000000  -1.824520683146258   0.835012167790563
   1.000000000000000   2.000000000000000   1.000000000000000   1.000000000000000  -1.825351261746257   0.854128332434601
   1.000000000000000   2.000000000000000   1.000000000000000   1.000000000000000  -1.845749373866514   0.899792317177862
   1.000000000000000   2.000000000000000   1.000000000000000   1.000000000000000  -1.890243419701735   0.963689345198141
   1.000000000000000  -2.000000000000000   1.000000000000000   1.000000000000000  -1.989176997083584   0.989218209927750
   1.000000000000000  -2.000000000000000   1.000000000000000   1.000000000000000  -1.996496707908275   0.996511870590091
   1.000000000000000  -2.000000000000000   1.000000000000000   1.000000000000000  -1.998714416931744   0.998722644911976
   1.000000000000000  -2.000000000000000   1.000000000000000   1.000000000000000  -1.999653030269727   0.999659262704001
gain =
    4.556034632804534e-009