We present new and precise angular diameter measurements of the long-p
eriod variable R Leonis at 833 and 903 nm. Our inferred photospheric d
iameter (38 +/- 2.5 mas) and stellar effective temperature (2459 +/- 1
50 K) are both in good agreement with recent determinations made at th
e same variability phase in the near-infrared. Assuming a parallax of
8.3 mas, we derive a stellar radius of 495 R.. This far exceeds the ra
nge of theoretical predictions for fundamental-mode pulsation (200 +/-
50 R.), and thus requires that R Leonis pulsates in the first- or a h
igher overtone mode. The expected availability of high-quality paralla
x measurements from the Hipparcos satellite and state-of-the-art groun
d-based instruments suggests that similar mode identification will be
possible for a dozen or more nearby Mira-type variables.