The Carnegie Hubble Program ( CHP ) is designed to calibrate the extragalactic distance scale using data from the post-cryogenic era of the Spitzer Space Telescope . The ultimate goal of the CHP is a systematic improvement in the distance scale leading to a determination of the Hubble Constant to within an accuracy of 2 % . This paper focuses on the measurement and calibration of the Galactic Cepheid Period-Luminosity ( Leavitt ) Relation using the warm Spitzer IRAC 1 and 2 bands at 3.6 and 4.5 \mu m. We present photometric measurements covering the period range 4 - 70 days for 37 Galactic Cepheids . Data at 24 phase points were collected for each star . Three PL relations of the form M = a ( \log ( P ) -1 ) + b are derived . The method adopted here takes the slope a to be -3.31 , as determined from the Spitzer LMC data of Scowcroft et al . ( 2012 ) . Using the geometric HST guide-star distances to ten Galactic Cepheids we find a calibrated 3.6 \micron PL zero-point of -5.80 \pm 0.03 . Together with our value for the LMC zero-point we determine a reddening-corrected distance modulus of 18.48 \pm 0.04 mag to the LMC . The mid-IR Period-Color diagram and the [ 3.6 ] - [ 4.5 ] color variation with phase are interpreted in terms of CO absorption at 4.5 \micron . This situation compromises the use of the 4.5 \micron data for distance determinations .