A chain antimony oxide fine particle group comprising antimony oxide fine particles which have an average particle diameter of 5 to 50 nm, are connected in the form of a chain and have an average connection number of 2 to 30 and preferably used for forming a hard coating film. The fine particle group can be prepared by a process comprising treating an alkali antimonate aqueous solution with a cation exchange resin to prepare an antimonic acid (gel) dispersion and then treating the dispersion with an anion exchange resin and/or adding a base to the dispersion. Also provided is a substrate with a film comprising a substrate and a hard coating film. The hard coating film includes a chain inorganic oxide fine particle group, in which inorganic oxide fine particles of 2 to 30 on the average are connected in the form of a chain, and a matrix. The inorganic oxide particles may be silica particles, silica-alumina particles being preferable, and porous particles and/or hollow particles having a cavity inside being more preferable.