Semiconductor nanoplatelets (NPLs) are planar nanocrystals that have recently attracted considerable attention due to their quantum-well-like physics, atomically precise thickness, and unique photophysical properties such as narrow-band fluorescence emission. These attributes are of potential interest for applications in biomolecular and cellular imaging, but it has been challenging to colloidally stabilize these nanocrystals in biological media due to their large dimensions and tendency to aggregate. Here we introduce a new colloidal material that is a hybrid between a NPL and an organic nanodisc composed of phospholipids and lipoproteins. The phospholipids adsorb to flat surfaces on the NPL, and lipoproteins bind to sharp edges to enable monodisperse NPL encapsulation with long-term stability in biological buffers and high-salt solutions. The lipoprotein NPLs (L-NPLs) are highly fluorescent, with brightness comparable to that of wavelength-matched quantum dots at both the ensemble and single-molecule levels. They also exhibit a unique feature of rapid internalization into living cells, after which they retain their fluorescence. These unique properties suggest that L-NPLs are particularly well suited for applications in live-cell single-molecule imaging and multiplexed cellular labeling.