We have investigated the magnetic, dielectric, and magnetodielectric (MDE) behavior of a geometrically frustrated spin-chain system, Ca3Co1.4Rh0.6O6 (related to Ca3CoRhO6), in the single crystalline form for different orientations. The results bring out that the magnetic behavior of this compound is by itself interesting in the sense that this compound exhibits an anisotropic glassy-like magnetic behavior with a huge frequency (ν) dependence of ac susceptibility (χ) peak for an orientation along the spin-chain in the range of 30–60 K; this behavior is robust to applications of large external magnetic fields (H) unlike in canonical spin-glasses. The temperature dependence of dielectric constant also shows strong ν-dependence with similar robustness to H. The isothermal H-dependent dielectric results at low temperatures establish anisotropic MDE coupling. It is intriguing to note that there is a “step” roughly at one-third of saturation values as in the case of isothermal magnetization curves for same temperatures (for orientation along spin-chain), a correlation hitherto unrealized for geometrically frustrated systems.