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Abstract Continuing extreme downscaling of semiconductor devices, essential for high performance and energy efficiency of future microelectronics, hinges on extreme ultraviolet lithography (EUVL) and addressing associated challenges. One of such challenges is a need for improved EUV photoresists featuring simultaneously high sensitivity, resolution, and etch selectivity. Here, a new, positive‐tone, organic–inorganic hybrid EUV photoresist is demonstrated that delivers a high‐resolution EUVL and electron‐beam lithography (EBL) patterning capability combined with high sensitivity and etch resistance. The new resist, poly(methyl methacrylate) infiltrated with indium oxide (PMMA‐InOx), is synthesized via vapor‐phase infiltration (VPI), a material hybridization technique derived from atomic layer deposition. The weak binding of the gaseous indium precursor, trimethylindium, to the carbonyl group in PMMA allows the synthesis of hybrids with inorganic content distributed uniformly in the resist, enabling high EUVL and EBL sensitivities (18 mJ cm−2 and 300 µC cm−2, respectively) and high‐resolution positive‐tone EUVL patterning (e.g., 40 nm half‐pitch line‐space and 50 nm diameter contact hole patterns) with high Si etch selectivity (>30–40). The low exposure doses required to pattern the PMMA‐InOx hybrid resist, high etch resistance, and processing strategies, which are developed, can pave the way for using infiltration‐synthesized hybrid thin films as reliable positive‐tone EUV photoresists for future semiconductor patterning.