Proxima Centauri, the nearest star to the sun, hosts a habitable-zone planet (Anglada-Escude' et al. 2016 Nature 536, 437). Several teams have sought Proxima b's transits using ground-based photometry, and have reported tentative transit detections (Liu et al. 2018 AJ 155, 12; Blank et al. 2018 AJ 155, 228; others). Proxima, a modest-sized M-dwarf star, flares at the 0.5% level (the predicted Proxima b transit depth) 63 times per day, according to our team's prior analysis of optical photometry from the Microvariability and Oscillations of STars spacecraft (Davenport et al. 2016 ApJL 829, L31). This dramatically limits optical precision. However, the effect of flares is much reduced in the infrared. We observed the system with the Spitzer Space Telescope's Infrared Array Camera in November 2016. Our first observation was a 48-hour stare at 4.5 um. It was centered on the predicted transit and covered the 99% credible region for the transit time, based on the discovery radial-velocity (RV) data. Despite a transit-depth precision of 0.01% for a 1 hour transit, we did not detect the predicted 0.5% transit. There was structure in the light curve, including some asymmetric transit-like features, that led us to conduct follow-up observations in May, June, July, and November 2017. None of these observations contained detections, once we accounted for a new manifestation of systematics due to spacecraft vibration. Our improved methods for identifying and partly removing this effect is the topic of the next presentation. This work is based on observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA. We acknowledge support from: NASA Planetary Atmospheres Program grant NNX12AI69G, NASA Astrophysics Data Analysis Program grant NNX13AF38G. CATA-Basal/Chile PB06 Conicyt and Fondecyt/Chile project #1161218 (JSJ). Spanish MINECO programs AYA2016-79245-C03-03-P (PJA, CRL, and ER) and ESP2017-87676-C05-02-R (ER).