We report the first observation of a sharp heat-capacity signature related to the superfluid transition in thin 4 He films adsorbed on porous Vycor and xerogel glasses. The transition temperatures of these films range from 0.14 to 1.1 K. This new feature is found in addition to the broad peak centered at a higher temperature reported in a number of earlier studies.PACS numbers: 67.40. Kh, 67.40.Hf, 67.40.Rp, The confinement of He in a multiply connected geometry such as porous glass has received renewed experimental 1,2 as well as theoretical interest. 3 " 6 Superfluid density (p s ) measurements 1,2 of 4 He films in porous Vycor glass (pore diameter -70 A) reveal a sharp transition at T c with an asymptotic power-law dependence similar to the bulk X transition, i.e.,This behavior was seen for films with T c > 70 mK up to full pores where T c = 1.955 K (Refs. 1 and 2). More recently, studies of 4 He in two other porous glasses have revealed different exponents: 0.89 for 10" 3