The energy confinement time of TCV Ohmic, L-mode discharges is observed to depend strongly on the plasma shape, improving slightly with elongation and degrading strongly as triangularity is increased from zero to positive values. The thermal conductivity of these plasmas is found to be independent of the shape. This observation, combined with geometrical effects on the temperature gradient and a degradation with increasing input energy flux, can explain the observed variation in the energy confinement time.