Why is Chandrasekar Limit expressed relative to Sun?
The mass of the sun is just a unit of convenience in a astronomy. The sun's mass and luminosity, in particular, are relatively easy for us to measure precisely, and when we're talking about stars, provide a convenient scale where the numbers won't be too "astronomical" (be too high a power of $10$ to picture easily). You could derive the Chandrasekhar limit in grams, kilograms, or slugs from the relevant physics, if you wanted. The relevant equation (from the Wikipedia article) is:
$$M_{\mathrm{limit}} = \frac{\omega_3^0 \sqrt{3\pi}}{2} \left(\frac{\hbar c}{G}\right)^{3/2} \frac{1}{(\mu_e m_\mathrm{H})^2},$$
where $\mu_e$ is the average molecular weight per electron (stellar composition dependent), $m_\mathrm{H}$ is the mass of hydrogen, and $\omega_3^0$ is a numerical constant that is approximately $2.018236\ldots$.

It should be noted that the Chandrasekhar limit is a limit on the mass of the final white dwarf, not of the object that will produce the white dwarf.