We find that a structural solid-solid phase transition in a two-dimensional
Langmuir film is accompanied by strong positional disorder. Specifically,
we find by a grazing-incidence x-ray diffraction experiment that in monolay
ers of octadecanol both the hexagonal phase LS and the centered rectangular
(distorted hexagonal) phase S have algebraic decay of positional correlati
ons. The positional disorder is evidenced by variations of the exponent eta
, which drastically increases at the transition. The disorder is attributed
to elastic distortions around pretransitional fluctuations.