We discuss MAXIPOL, a bolometric balloon-borne experiment designed to measure the E-mode polarization of the cosmic microwave background radiation (CMB). MAXIPOL is the first bolometric CMB experiment to observe the sky using rapid polarization modulation. To build MAXIPOL, the CMB temperature anisotropy experiment MAXIMA was retrofitted with a rotating half-wave plate and a stationary analyzer. We describe the instrument, the observations, the calibration, and the reduction of data collected with 12 polarimeters operating at 140 GHz and with a FWHM beam size of 10'. We present maps of the Q and U Stokes parameters of an 8 deg2 region of the sky near the star β UMi. The power spectra computed from these maps give weak evidence for an EE signal. The maximum likelihood amplitude of l(l+1)CEEl/2π is 55+51-45 μK2 (68%), and the likelihood function is asymmetric and skewed positive such that with a uniform prior the probability that the amplitude is positive is 96%. This result is consistent with the expected concordance ΛCDM amplitude of 14 μK2. The maximum likelihood amplitudes for l(l+1)CBBl/2π and l(l+1)CEBl/2π are -31+31-19 and 18+27-34 μK2 (68%), respectively, which are consistent with zero. All of the results are for one bin in the range 151<=l<=693. Tests revealed no residual systematic errors in the time or map domain. A comprehensive discussion of the analysis of the data is presented in a companion paper.