Crystallization and growth of an isolated extended chain single crystal (ECSC) of polyethylene (PE) under high pressure from the melt into the mobile phase, such as hexagonal phase, was studied by in-situ optical microscopy and transmission electron microscopy. Direct evidence is obtained that an isolated ECSC was formed from a folded chain single crystal through the combination of newly recognized "lamellar thickening growth" and the long familiar lateral growth. This confirmed the prediction of chain sliding diffusion theory that the lamellar thickening growth takes place the important role in the origin of folded chain and extended chain crystals (FCCs and ECCs) presented by one of authors (M.H.) previously. The lamellar thickness (l) inceased linearly with time (t), indicating that the lamellar thickening growth rate is constant as long as the crystal is in isolation, i.e., it does not impinge on others, directly reflected also by the straightened taper of the cross-sectional shape. This is quite different from the well-known lamellar thickening of stacked-lamellar system where l increases linearly with logarithm of time (log t). It is shown that the difference is due to the difference between the primary and the secondary crystallization processes. The lamellar thickening growth rate (U), defined by (dl/dt). was measured for the first time by developing two method, "direct method" and "mapping method".