= Solution
The <polymer overlap concentration> is reached when there is roughly one chain per coil volume. If $M$ is the chain <molar mass>, choose the explicit geometric convention $V_{\mathrm{coil}}=4\pi R_g^3/3$, where $R_g$ is the <radius of gyration>. Then
$$
\boxed{c^*\simeq\frac{M}{N_A(4\pi/3)R_g^3}}.
$$
Here $c^*$ is mass per solution volume and $N_A$ is the <Avogadro constant>. A <good solvent> gives $R_g\propto N^\nu$ with $\nu\simeq0.588$, approximated by $3/5$ in the <Flory approximation>. With a <polystyrene> repeat-unit molar mass of about $104.15\,\mathrm{g\,mol^{-1}}$, the chain has approximately $N=960$ repeat units. This fixes the chain length but not the size amplitude: the problem supplies no statistical segment length or measured coil size.
For a numerical estimate, use the <good-solvent size calibration for polystyrene>,
$$
\frac{R_g}{\mathrm{nm}}\simeq0.0123\left[\frac{M}{\mathrm{g\,mol^{-1}}}\right]^{0.593}.
$$
This empirical calibration is quoted for benzene or toluene near room temperature at molar masses above $2\times10^5\,\mathrm{g\,mol^{-1}}$; using it here is a modest extrapolation to $M=10^5\,\mathrm{g\,mol^{-1}}$. It gives $R_g\simeq11.3\,\mathrm{nm}$. Thus
$$
c^*\simeq\frac{100\,\mathrm{kg\,mol^{-1}}}{(6.022\times10^{23}\,\mathrm{mol^{-1}})(4\pi/3)(11.3\times10^{-9}\,\mathrm m)^3}
\simeq\boxed{3\times10^1\,\mathrm{kg\,m^{-3}}\simeq3\times10^1\,\mathrm{g\,L^{-1}}}.
$$
The unrounded calibration gives about $27\,\mathrm{g\,L^{-1}}$. This is an estimate under a stated extra material input, not a unique number determined solely by molecular weight and the phrase good solvent. Choosing a different coil-volume convention changes its prefactor. The robust chain-length dependence is $c^*\propto M^{1-3\nu}\simeq M^{-4/5}$ for a flexible good-solvent coil.
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