Decreasing oil extraction stimulates attempts to use biologically available sources to produce polyols, which are the basic components for obtaining polyurethane foams. Plants are inexhaustible source of oils, sugars, starches, and cellulose. Similar substrates to obtain polyols are chitosans. Commercially available modified chitosans are soluble in water, which gives them the possibility to react with hydroxyalkylating agents. We used a water-soluble chitosan previously to obtain polyols suitable for producing rigid polyurethane foams. Here, we described hydroxyalkylation of a low-molecular-weight chitosan (oligomeric chitosan) with glycidol and ethylene carbonate to obtain polyols. The polyols were isolated and studied in detail by IR, 1H-NMR, and MALDI–ToF methods. Their properties, such as density, viscosity, surface tension, and hydroxyl numbers, were determined. The progress of the hydroxyalkylation reaction of water-soluble chitosan and chitosan oligomer with glycidol was compared in order to characterize the reactivity and mechanism of the process. We found that the hydroxyalkylation of chitosan with glycidol in glycerol resulted in the formation of a multifunctional product suitable for further conversion to polyurethane foams with favorable properties. The straightforward hydroxyalkylation of chitosan with glycidol was accompanied by the oligomerization of glycidol. The hydroxyalkylation of chitosan with glycidol in the presence of ethylene carbonate was accompanied by minor hydroxyalkylation of chitosan with ethylene carbonate. The chosen polyols were used to obtain rigid polyurethane foams which were characterized by physical parameters such as apparent density, water uptake, dimension stability, heat conductance, compressive strength, and heat resistance at 150 and 175 °C. The properties of polyurethane foams obtained from chitosan-oligomer and water-soluble-chitosan sources were compared. Polyurethane foams obtained from polyols synthesized in the presence of glycerol had advantageous properties such as low thermal conductivity, enhanced thermal resistance, dimensional stability, low water uptake, and high compressive strength, growing remarkably upon thermal exposure.