Carbyne is a one-dimensional monoatomistic chain of carbon atoms, consisting of repeating sp-hybridized groups – the extreme minimalist molecular rod or chain. Due to their potential use in atomic-scale circuits, there has been particular interest in their novel electronic and thermal properties and are promising platforms for heat dissipation. Potential 1D thermal transport is advantageous as the heat conduction can theoretically be directed along the molecule. However, the thermal properties of carbyne, essential to their successful application in the design of novel devices, have yet to be rigorously determined. Here, using full atomistic molecular dynamics (MD), we explore the thermal conductivity (κ) of a system of carbyne chains to enable statistical averaging. Müller-Plathe reverse perturbation method was used to obtain κ along the chain direction. For a freestanding chain with a length of approximately 40nm, we indicate an ultrahigh thermal conductivity of approximately 0.793kW/m-K, on the similar order of carbon nanotubes and graphene. Also, when we look into the thermal conductivity by atomistic weight, the carbyne model we use obtains a higher value than (5, 5) CNT and is comparable to graphene nanoribbon, which indicates very promising thermal conduction. Moreover, chains of varying length and strain are simulated individually to systematically explore the accessible range of conductivities. The thermal conductivity decreases when more strain applied, while it is significantly enhanced when we add more atoms to the carbyne chains. Additionally, we reported a close-to-linear relationship between κ and chain length, which provided supportive evidence for the controlling of thermal conductivity of carbyne.