To use observed transneptunian objects (TNOs) to constrain models of the early solar system, they first must be classified. We classify TNOs into dynamical classes of resonant, classical, scattering, and detached objects by assessing the time series of the numerical propagation of their observed orbits. Resonant TNOs are of particular interest because their relative populations and distribution within Neptune's resonances are sensitive to the nature of giant planet migration. However the sheer number of potential resonances with Neptune and the complexity of dynamical behaviors in resonances can make it difficult to definitively classify TNOs as resonant or non-resonant using simple criteria. We have typically relied on human-intensive procedures involving visual inspection of numerical integration results to provide the most accurate classifications. This approach already limits our ability to quantify the uncertainties in the classifications of those observed TNOs with large orbital uncertainties. It is also not sustainable in the face of the large number of TNO discoveries expected with LSST. Thankfully machine learning (ML) provides a solution to this problem. We have trained and tested a gradient boosting classifier on ~15,000 TNO orbits (~10,000 based on observed TNO orbits, ~5000 based on fictitious orbits). We provide the classifier with a wide range of dynamically meaningful data features calculated from 0.5 and 10 Myr integrations of these orbits and program it to predict classifications based on the Gladman et al. 2008 nomenclature scheme. The classifier returns fully correct classifications in 97.3% of the cases and dynamically reasonable classifications in 99.6% of the cases (the latter accounts for cases of messy dynamical behavior where the classifier chose a label that describes at least part of the behavior). This ML classifier is available as part of the python-based Small Body Dynamics Tool (SBDynT; https://github.com/small-body-dynamics/SBDynT).