We fabricated a robust ultrathin film of a triblock copolymer, poly[styrene-b-(ethylene-co-butylene)-b-styrene] (SEBS), functionalized with 2% of maleic anhydride by melt/solution grafting to a chemically reactive silicon surface. We used epoxy-terminated self-assembling monolayers to functionalize silicon surface. The thickness of grafted block polymer, t, was varied from 1.35 to 9.1 nm to test the limits of stability of microphase-separated structures of the triblock copolymer tethered under confined conditions. Accordingly, the ratio tid was changed from 0.05 to 0.33, where d is the interdomain spacing. The contact angle measurements demonstrated that the surface of the complete block copolymer films was totally occupied by poly[ethylene-co-butene] (PEB) chains. When the SEES film thickness reached 8.4 nm, the film possessed the well-defined microphase structure of the typical thermoplastic elastomer material, where PS phase formed the microdomain network that reinforced the elastomeric matrix. The microphase separation was completely suppressed only for ultrathin films with t/d < 0.08. We found that tethered block copolymer monolayers were extremely stable and preserved their microdomain structure at elevated temperatures unlike physically adsorbed films that dewetted under similar conditions.