We measure host galaxy photometry and local fluxes within 3 kpc for 882 Type Ia supernov\ae\ (SNIa) spanning the redshift range $0.01 < z < 1$ and use SED fitting techniques to derive host properties such as stellar masses and local $U-V$ rest-frame colors. The latter is an indicator of the luminosity weighted age of the stellar population in a galaxy. We find that local $U-V$ color brightness dependence is at least as significant as it is for properties of the host galaxy as a whole (host stellar mass or global $U-V$ rest-frame color). Once selection requirements are chosen, we perform cosmological fits using local color as a third standardization variable and find its step significance at the level of $7\sigma$, indicating that the remaining luminosity variations in SNIa samples can be reduced using a third standardization variable taking the local environment into account. Even after a mass step correction, a correlation of $4.6\sigma$ is found between local $U-V$ color and Hubble diagram residuals. %Correcting from mass step, we find a remaining $4.6\sigma$ correlation of local color with the corresponding Hubble diagram residuals. We find that using the local color in place of the stellar mass results in a change in the measured value of the dark energy equation of state parameter of 0.6\%. The precise analysis of local environment of SNIa will be of great importance for the forthcoming surveys, and in particular LSST for which uncertainties on the dark energy equation of state will be comparable to the reported effects.