At least 15% of the low-FeO chondrules in Semarkona (LL3.0) have mesostases that are concentrically zoned in Na, with enrichments near the outer margins. We have studied zoned chondrules using electron microprobe methods (x-ray mapping plus quantitative analysis), ion micropobe analysis for trace elements and hydrogen isotopes, cathodoluminescence imaging, and transmission electron microscopy in order to determine what these objects can tell us about the environment in which chondrules formed and evolved. Mesostases in these chondrules are strongly zoned in all moderately volatile elements and H (interpreted as water). Calcium is depleted in areas of volatile enrichment. Titanium and Cr generally decrease toward the chondrule surfaces, whereas Al and Si may either increase or decrease, generally in opposite directions to one another; Mn follows Na in some chondrules but not in others; Fe and Mg are unzoned. D/H ratios increase in the water-rich areas of zoned chondrules. Mesostasis shows cathodoluminescence zoning in most zoned chondrules, with the brightest yellow color near the outside. Mesostasis in zoned chondrules appears to be glassy, with no evidence for devitrification. Systematic variations in zoning patterns among pyroxene- and olivine-rich chondrules may indicate that fractionation of low- and high-Ca pyroxene played some role in Ti, Cr, Mn, Si, Al, and some Ca zoning. But direct condensation of elements into hot chondrules, secondary melting of late condensates into the outer portions of chondrules, and subsolidus diffusion of elements into warm chondrules cannot account for the sub-parallel zoning profiles of many elements, the presence of H2O, or elemental abundance patterns. Zoning of moderately volatile elements and Ca may have been produced by hydration of chondrule glass without devitrification during aqueous alteration on the parent asteroid. This could have induced structural changes in the glass allowing rapid diffusion and exchange of elements between altered glass and surrounding matrix and rim material. Calcium was mainly lost during this process, and other nonvolatile elements may have been mobile as well. Some unzoned, low-FeO chondrules appear to have fully altered mesostasis.