The redshift drift of objects moving in the Hubble flow has been proposed as a powerful model-independent probe of the underlying cosmology . A measurement of the first and second order redshift derivatives appears to be well within the reach of upcoming surveys using ELT-HIRES and the SKA Phase 2 array . Here we show that an unambiguous prediction of the R _ { h } = ct cosmology is zero drift at all redshifts , contrasting sharply with all other models in which the expansion rate is variable . For example , multi-year monitoring of sources at redshift z = 5 with the ELT-HIRES is expected to show a velocity shift \Delta v = -15 cm s ^ { -1 } yr ^ { -1 } due to the redshift drift in Planck \Lambda CDM , while \Delta v = 0 cm s ^ { -1 } yr ^ { -1 } in R _ { h } = ct . With an anticipated ELT-HIRES measurement error of \pm 5 cm s ^ { -1 } yr ^ { -1 } after 5 years , these upcoming redshift drift measurements might therefore be able to differentiate between R _ { h } = ct and Planck \Lambda CDM at \sim 3 \sigma , assuming that any possible source evolution is well understood . Such a result would provide the strongest evidence yet in favour of the R _ { h } = ct cosmology . With a 20 -year baseline , these observations could favor one of these models over the other at better than 5 \sigma .