  A leading theoretical expectation for the final stages of planet formation is
that disk migration should naturally drive orbits into chains of mean motion
resonances (MMRs). In order to explain the dearth of MMR chains observed at Gyr
ages ($<1\%$), this picture requires such configurations to destabilize and
scramble period ratios following disk dispersal. Strikingly, the only two known
stars with three or more planets younger than $\lesssim 100$ Myrs, HR 8799 and
V1298 Tau, have been suggested to be in such MMR chains, given the orbits'
near-integer period ratios. We incorporate recent transit and radial velocity
observations of the V1298 Tau system, and investigate constraints on the
system's orbital architecture imposed by requiring dynamical stability on
timescales much shorter than the system's age. We show that the recent
radial-velocity mass measurement of V1298 Tau $b$ places it within a factor of
two of the instability limit, and that this allows us to set significantly
lower limits on the eccentricity ($e_b \leq 0.17$ at $99.7\%$ confidence).
Additionally, we rule out a resonant chain configuration for V1298 Tau at
$\gtrsim 99\%$ confidence. Thus, if the $\sim 23$ Myr-old V1298 Tau system did
form as a resonant chain, it must have undergone instability and rearrangement
shortly after disk dispersal. We expect that similar stability constrained
characterization of future young multi-planet systems will be valuable in
informing planet formation models.
