We present results from two observations of the cosmic microwave background (CMB) performed from the South Pole during the 1993-1994 austral summer. Each observation employed a 3 deg peak-to-peak sinusoidal, single-difference chop and consisted of a 20 deg x 1 deg strip on the sky. The first observation used a receiver which operates in three channels between 38 and 45 GHz (Q-band) with a full width half maximum (FWHM) beam which varies from 1 deg to 1.15 deg. The second observation overlapped the first observation and used a receiver which operates in four channels between 26 and 36 GHz (Ka-band) with a FWHM beam which varies from 1.5 deg to 1.7 deg. Significant correlated structure is observed in all channels for each observation. The spectrum of the structure is consistent with a CMB spectrum and is formally inconsistent with diffuse synchrotron and free-free emission at the 5 sigma level. The amplitude of the structure is inconsistent with 20 K interstellar dust; however, the data do not discriminate against flat or inverted spectrum point sources. The root mean square amplitude (+/- 1 sigma) of the combined (Ka + Q) data is Delta T(sub rms) = 41.2(sup +15.5, sub -6.7) micro-K for an average window function which has a peak value of 0.97 at l = 68 and drops to e(exp -0.5) of the peak value at l = 36 and l = 106. A band power estimate of the CMB power spectrum, C(sub l), gives average value of (C(sub l)l(l + 1)/(2 pi))(sub B) = 1.77(sup +1.58, sub -0.54) x 10(exp -10).