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We report measurements of the magnetic penetration depth $\ensuremath{\lambda}$ in single crystals of ${\mathrm{P}\mathrm{r}\mathrm{O}\mathrm{s}}_{4}{\mathrm{S}\mathrm{b}}_{12}$ down to 0.1 K, with the ac field applied along the $a$, $b$, and $c$ directions. In all three field orientations, $\ensuremath{\lambda}\ensuremath{\sim}{T}^{2}$ and superfluid density ${\ensuremath{\rho}}_{s}\ensuremath{\sim}{T}^{2}$ for $T<0.3{T}_{c}$. Data are best fit by the $^{3}\mathrm{H}\mathrm{e}$ A-phase-like …