Previous studies of ordinary chondrites (OC) reported isolated microchondrules within the fine-grained or clastic matrix of many type-3 samples; larger sets of microchondrules have also been found as rare clasts in type-3 OC. We report here another major setting for microchondrules; large numbers (n ≥ 100) of microchondrules (≤40 μm in apparent diameter) occur together with irregularly shaped fragments in fine-grained rims around four low-FeO porphyritic olivine chondrules and one barred olivine chondrule. These chondrules are from LL3.1 Bishunpur, L3.4 EET90161, L3.4 EET90261, LL3.4 Piancaldoli, and LL3.0 Semarkona. The two kinds of microchondrules observed are (1) numerous low-FeO radial and cryptocrystalline microchondrules consisting of low-Ca pyroxene and (2) relatively rare high-FeO olivine microchondrules. Both types of microchondrules are embedded in high-FeO fine-grained matrix materials; they are typically accompanied by irregularly shaped pyroxene fragments that form a continuum in composition and shape with the low-FeO microchondrules. The pyroxene-rich surfaces of the host chondrules project into the surrounding rims as peninsulas with rounded embayments, consistent with remelting; although on average less ferroan, the peninsulas overlap the fragments and low-FeO microchondrules in composition and appear to have been the main source of these objects. The occurrence of numerous low-FeO pyroxene-rich microchondrules with similar textures and compositions within high-FeO fine-grained matrix rims around normal-size chondrules and the apparent remelting of the surfaces of the host chondrules indicate that the microchondrules formed after solidification of the host chondrules mainly by remelting of their pyroxene-rich surfaces (or, possibly, igneous rims). The remnants of these pyroxene-rich rims are preserved as peninsulas extending outward from the chondrule surface and as irregularly shaped pyroxene fragments coexisting with the microchondrules. Because a newly formed microchondrule "cloud" in the nebula would dissipate quickly due to random motions of the individual microchondrules, it seems inescapable that the fine-grained material, which now surrounds the microchondrules, was in their immediate vicinity when they formed and served as a trapping matrix. The material probably occurred as a highly porous, aerogel-like aggregate of FeO-rich nebular dust. The rare high-FeO olivine microchondrules probably formed at the same time as the low-FeO pyroxene microchondrules by melting adjacent portions of the porous dust.