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Using a sample of 119 QSOs, containing objects we have selected having previously available high quality ground-based and IUE spectral observations, together with Hubble Space Telescope (HST) observations of 26 QSOs from Bahcall et al. (1993, 1995) and Impey et al. (1995) and new optical observations of 41 objects by Steidel & Sargent (1995), we study the redshift evolution of Lyman limit absorption systems (LLSs; tau greater than 1.0) over the reshift range 0.32 less than or equal to z(sub LLS) less than or equal to 4.11. The HST observations significantly improve the determination of the low redshift (0.4 less than or equal to z(sub LLS) less than or equal to 1.4) distribution. We find the effect which may have been responsible for the apparent strong evolution at a(sub LLS) greater than or equal to 2.5 found by Lanzetta (1991), which led him to consider a broken, not single power law as a better description of the redshift distribution of LLSs. After removing objects which may bias our sample, leaving a total of 169 QSOs, we find the distribution is well described by a single power law, and obtain for the number density as a function of redshift the form N(z) = N(sub 0)(1 + z)(exp gamma) with gamma = 1.50 =/- 0.39 and N(sub 0) = 0.25(sup -0.10)(sub +0.17), consistent with a constant comoving density of absorbers in a Firedmann universe with q(sub 0) = 0 but indicating evolution if q(sub 0) = 1/2.