We present a Chandra observation of the cooling flow cluster Abell 262. Spectral fits show that the intracluster medium (ICM) in A262 cools by a factor of three from 2.7 keV to 0.9 keV at the cluster center. A mass deposition rate of Mdot = 19 +6/-5 Msun/yr is measured. Complex structure is found in the very inner regions of the cluster, including knots of emission and a clear deficit of emission to the east of the cluster center. The bright X-ray structures are located in the same regions as optical line emission, indicating that cooling to low temperatures has occurred in these regions. The X-ray deficit is spatially coincident with the eastern radio lobe associated with the active galactic nucleus hosted by the central cD galaxy. The region surrounding the X-ray hole is cool, and shows no evidence that it has been strongly shocked. This joins the ranks of other cooling flow clusters with Chandra-detected bubbles blown by central radio sources. This source is different than the other well-known cases, in that the radio source is orders of magnitude less luminous and has produced a much smaller bubble. Comparing the energy output of the radio source with the luminosity of the cooling gas shows that energy transferred to the ICM from the radio source is insufficient to offset the cooling flow unless the radio source is currently experiencing a less powerful than average outburst, and was more powerful in the past.