  The Carnegie Hubble Program (CHP) is designed to improve the extragalactic
distance scale using data from the post-cryogenic era of Spitzer. The ultimate
goal is a determination of the Hubble constant to an accuracy of 2%. This paper
is the first in a series on the Cepheid population of the Large Magellanic
Cloud, and focusses on the period-luminosity relations (Leavitt laws) that will
be used, in conjunction with observations of Milky Way Cepheids, to set the
slope and zero--point of the Cepheid distance scale in the mid-infrared. To
this end, we have obtained uniformly-sampled light curves for 85 LMC Cepheids,
having periods between 6 and 140 days. Period-luminosity and period-color
relations are presented in the 3.6 \mu m and 4.5\mu m bands. We demonstrate
that the 3.6 \mu m band is a superb distance indicator. The cyclical variation
of the [3.6]-[4.5] color has been measured for the first time. We attribute the
amplitude and phase of the color curves to the dissociation and recombination
of CO molecules in the Cepheid's atmosphere. The CO affects only the 4.5 \mu m
flux making it a potential metallicity indicator.
