We demonstrate a noncontact thermal microprobe technique for measuring the thermal conductivity κ with ∼3 μm lateral spatial resolution by exploiting quasiballistic air conduction across a 10-100 nm air gap between a joule-heated microprobe and the sample. The thermal conductivity is extracted from the measured effective thermal resistance of the microprobe and the tip-sample thermal contact conductance and radius in the quasiballistic regime determined by calibration on reference samples using a heat transfer model. Our κ values are within 5%-10% of that measured by standard steady-state methods and theoretical predictions for nanostructured bulk and thin film assemblies of pnictogen chalcogenides. Noncontact thermal microprobing demonstrated here mitigates the strong dependence of tip-sample heat transfer on sample surface chemistry and topography inherent in contact methods, and allows the thermal characterization of a wide range of nanomaterials.