Orthogonal-frequency-division multiplexing (OFDM) transforms a frequency-selective multiple-input multiple-output (MIMO) fading channel into a MIMO-OFDM channel that has a well-defined outage capacity. A transmitter with channel knowledge can achieve this capacity by a combination of eigenbeamforming and water-filling; the eigenbeamforming transforms the MIMO-OFDM channel into a parallel bank of scalar channels, and the water-filling procedure optimally allocates rate and energy to the scalar channels - a form of adaptive modulation. This paper shows that the water-filling procedure is not necessary to approach the zero-outage capacity of the MIMO-OFDM channel; it is sufficient instead to use a combination of eigenbeamforming and a fixed (nonadaptive) rate allocation. The fixed allocation depends only on the statistics of the channel and is independent of the particular channel realization. This paper proves that the capacity penalty incurred by the fixed allocation approaches zero as the number of antennas grows large. Numerical results indicate that the convergence is fast; for example, the fixed allocation suffers an SNR penalty of less than 0.2 dB for a 6-input 6-output Rayleigh-fading MIMO-OFDM channel at 8 bits per signaling interval, when the channel is assumed to be uncorrelated between antennas and between channel taps. A main conclusion is that eigenbeamforming is the most valuable way to exploit knowledge of the channel at the transmitter, and that any subsequent adaptive modulation has minimal relative value.