  Convergent disk migration has long been suspected to be responsible for
forming planetary systems with a chain of mean-motion resonances (MMR).
Dynamical evolution over time could disrupt the delicate resonant
configuration. We present TOI-1136, a 700-Myr-old G star hosting at least 6
transiting planets between $\sim$2 and 5 $R_\oplus$. The orbital period ratios
deviate from exact commensurability by only $10^{-4}$, smaller than the
$\sim$\,$10^{-2}$ deviations seen in typical Kepler near-resonant systems. A
transit-timing analysis measured the masses of the planets (3-8$M_\oplus$) and
demonstrated that the planets in TOI-1136 are in true resonances with librating
resonant angles. Based on a Rossiter-McLaughlin measurement of planet d, the
star's rotation appears to be aligned with the planetary orbital planes. The
well-aligned planetary system and the lack of detected binary companion
together suggest that TOI-1136's resonant chain formed in an isolated,
quiescent disk with no stellar fly-by, disk warp, or significant axial
asymmetry. With period ratios near 3:2, 2:1, 3:2, 7:5, and 3:2, TOI-1136 is the
first known resonant chain involving a second-order MMR (7:5) between two
first-order MMR. The formation of the delicate 7:5 resonance places strong
constraints on the system's migration history. Short-scale (starting from
$\sim$0.1 AU) Type-I migration with an inner disk edge is most consistent with
the formation of TOI-1136. A low disk surface density ($\Sigma_{\rm
1AU}\lesssim10^3$g~cm$^{-2}$; lower than the minimum-mass solar nebula) and the
resultant slower migration rate likely facilitated the formation of the 7:5
second-order MMR. TOI-1136's deep resonance suggests that it has not undergone
much resonant repulsion during its 700-Myr lifetime. One can rule out rapid
tidal dissipation within a rocky planet b or obliquity tides within the largest
planets d and f.
