Convergent disk migration has long been suspected to be responsible for forming planetary systems with a chain of mean-motion resonances (MMRs). Dynamical evolution over time could disrupt the delicate resonant configuration. We present TOI-1136, a 700{+/-}150Myr old G-star hosting at least six transiting planets between ~2 and 5 R{Earth}. The orbital period ratios deviate from exact commensurability by only 10^-4^, smaller than the ~10^-2^ deviations seen in typical Kepler near-resonant systems. A transit-timing analysis measured the masses of the planets (3-8M{Earth}) 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 a detected binary companion together suggest that TOI-1136's resonant chain formed in an isolated, quiescent disk with no stellar flyby, 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 MMRs. The formation of the delicate 7:5 resonance places strong constraints on the system's migration history. Short-scale (starting from ~0.1au) Type-I migration with an inner disk edge is most consistent with the formation of TOI-1136. A low disk surface density ({Sigma}1au<~103g/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.