An IC socket (FIGS. 2, 14) is provided with a core block (9) for supporting a multitude of contact pins (13, 14). A TAB package including a chip (T) and a film (PCB) having lead terminals arranged at a fine pitch is to be placed into the socket for engagement with upper ends of the contacts (13, 14) and is to be pressed downwardly by a cover (2). Inner and outer floating and vertically displaceable members (10, 11) are spring biased upwardly against the TAB package and separating members (12) are located along each side of the socket and are floatably supported by upper ends of the contact pins (13, 14). The separating members (12) include series of ribs (12e, 12f) on opposite sides for maintaining alignment of the upper ends of the contact pins. The socket also includes heat transfer pins (8). The core plate (9) includes ribs (9f, 9g, 9h, 9i, 9j) for positioning central sections of the contact pins (13, 14). In another embodiment (FIGS. 21, 33, 34) an inner floating member (17) and an outer floating member (18) are each formed with series of ribs (17f, 18c) for alignment of upper ends (21d, 21f) of the contacts (20, 21). The floating members (17, 18) may be integrally joined by pins (19). In other embodiments, (FIGS. 52, 54, 58, 60, 61) a floating member (46) biased upwardly by a spring (23) and a group of floatably supported separating members (47, 48) are each formed with series of ribs for alignment of upper ends of the contacts.