While we optically observed the pressure-induced transformation between the solid phases of SII and SI of n-heptadecane, of which p-T diagram has a parallel and wide gap between the coexistence lines between liquid-SI and between SI-SII (the same as that of n-pentadecane), we found that the SII crystal of n-heptadecane is stable even below the coexisting line between the SI and liquid, as is that of n-pentadecane. Fortunately, we can easily distinguish the SI crystal, of which morphology shows a hexagonal thin plate with very round corners, from the SII crystal, of which morphology shows a long and narrow pillar-like form in the liquid. Here, we report on the epitaxial growth of SI filmy crystals of n-heptadecane on its SII crystal in the p-T condition of 40 MPa and 30 °C. Although we could not observe the epitaxial growth of n-pentadecane, we could observe the clear epitaxial growth of n-heptadecane in the mixed liquid of n-pentadecane and n-heptadecane. Growth suppression by n-pentadecane brings about clear crystal shapes. Moreover, the epitaxially growing SI filmy crystals of n-heptadecane form a disk-like vessel which put its pillar-like SII crystal between the filmy crystals. If several billion years ago this vessel had been formed in a mixed drop of normal alkanes drifting about above the bottom of a deep sea, where the p-T condition was 40 MPa and 30 °C, the vessel might be seen as a cradle of primitive life.