The cooling rate of young neutron stars gives direct insight into their internal makeup .
Although the temperatures of several young neutron stars have been measured , until now a young neutron star has never been observed to decrease in temperature over time .
We fit 9 years of archival { \it Chandra } ACIS spectra of the likely neutron star in the \sim 330 years old Cassiopeia A supernova remnant with our non-magnetic carbon atmosphere model .
Our fits show a relative decline in the surface temperature by 4 % ( 5.4 \sigma , from 2.12 \pm 0.01 \times 10 ^ { 6 } K in 2000 to 2.04 \pm 0.01 \times 10 ^ { 6 } K in 2009 ) and observed flux ( by 21 % ) .
Using a simple model for neutron star cooling , we show that this temperature decline could indicate that the neutron star became isothermal sometime between 1965 and 1980 , and constrains some combinations of neutrino emission mechanisms and envelope compositions .
However , the neutron star is likely to have become isothermal soon after formation , in which case the temperature history suggests episodes of additional heating or more rapid cooling .
Observations over the next few years will allow us to test possible explanations for the temperature evolution .