The first limits on the prompt emission from the long gamma-ray burst (GRB) 130427A in the >100 GeV energy band are reported. GRB 130427A was the most powerful burst ever detected with a redshift z ≲ 0.5 and featured the longest lasting emission above 100 MeV. The energy spectrum extends at least up to 95 GeV, clearly in the range observable by the High Altitude Water Cherenkov (HAWC) Gamma-Ray Observatory, a new extensive air shower detector currently under construction in central Mexico. The burst occurred under unfavorable observation conditions, low in the sky and when HAWC was running 10% of the final detector. Based on the observed light curve at MeV-GeV energies, eight different time periods have been searched for prompt and delayed emission from this GRB. In all cases, no statistically significant excess of counts has been found and upper limits have been placed. It is shown that a similar GRB close to zenith would be easily detected by the full HAWC detector, which will be completed soon. The detection rate of the full HAWC detector may be as high as one to two GRBs per year. A detection could provide important information regarding the high energy processes at work and the observation of a possible cut-off beyond the Fermi Large Area Telescope energy range could be the signature of gamma-ray absorption, either in the GRB or along the line of sight due to the extragalactic background light.