Copropagating core and cladding modes in optical fibers can be coupled by a grating with a period greatly exceeding the wavelength, since their propagation constants are similar. In contrast to conventional longperiod gratings, in which the modulation is imposed by exposing a photosensitive core to ultraviolet light, we have created chiral long-period gratings with single- or double-helix symmetry by twisting optical fibers with nonconcentric or noncircular cores, respectively, as they pass through a short heat zone. The difference in symmetry between single- and double-helix gratings is manifested in their polarization properties. The use of these gratings as sensors of liquid level and temperature is demonstrated.