  The NASA telescope NICER has recently measured x-ray emissions from the
heaviest of the precisely known two-solar mass neutron stars, PSR J0740+6620.
Analysis of the data [Miller et al., Astrophys. J. Lett. 918, L28 (2021); Riley
et al., Astrophys. J. Lett. 918, L27 (2021)] suggests that PSR J0740+6620 has a
radius in the range of $R_{2.0} \approx (11.4-16.1)$ km at the $68\%$
credibility level. In this article, we study the implications of this analysis
for the sound speed in the high-density inner cores by using recent chiral
effective field theory ($\chi$EFT) calculations of the equation of state at
next-to-next-to-next-to-leading order to describe outer regions of the star at
modest density. We find that the lower bound on the maximum speed of sound in
the inner core, $\textbf{min}\{c^2_{s, {\rm max}}\}$, increases rapidly with
the radius of massive neutron stars. If $\chi$EFT remains an efficient
expansion for nuclear interactions up to about twice the nuclear saturation
density, $R_{2.0}\geqslant 13$ km requires $\textbf{min}\{c^2_{s, {\rm max}}\}
\geqslant 0.562$ and $0.442$ at the $68\%$ and $95\%$ credibility level,
respectively.
