See the supplementary material for materials and methods, TEM images of cell ultrastructure of Coscinodiscus oculus-iridis, time-lapse bright-field microscopy images showing the trapping and manipulation of a chloroplast within a small diatom cell, trapping potential and normalized autocorrelation analysis of chloroplast displacements, time-lapse bright-field microscopy images showing the trapping and manipulation of a small diatom cell, as well as chloroplasts for intracellular viscosity measurements, experiments demonstrating the effect of optical trapping on diatoms and organelles.