  Whereas many measurements in cosmology depend on the use of integrated
distances or time, galaxies evolving passively on a time scale much longer than
their age difference allow us to determine the expansion rate H(z) solely as a
function of the redshift-time derivative dz/dt. These model-independent `cosmic
chronometers' can therefore be powerful discriminators for testing different
cosmologies. In previous applications, the available sources strongly
disfavoured models (such as LambdaCDM) predicting a variable acceleration,
preferring instead a steady expansion rate over the redshift range 0 < z < 2. A
more recent catalog of 30 objects appears to suggest non-steady expansion. In
this paper, we show that such a result is entirely due to the inclusion of a
high, locally-inferred value of the Hubble constant H_0 as an additional datum
in a set of otherwise pure cosmic-chronometer measurements. This H_0, however,
is not the same as the background Hubble constant if the local expansion rate
is influenced by a Hubble Bubble. Used on their own, the cosmic chronometers
completely reverse this conclusion, favouring instead a constant expansion rate
out to z ~ 2.
