  We present the result of our extensive intranight optical monitoring of the
well known low-energy peaked BL Lac (LBL) object PKS 0735+178. This long-term
follow-up consists of $R$-band monitoring for a minimum duration of $\sim 4$
hours, on 17 nights spanning 11 years (1998-2008). Using the CCD as an N-star
photometer, a detection limit of around 1% was attained for the intra-night
optical variability (INOV). Remarkably, an INOV amplitude of $\geq 3%$ on
hour-like time scale was not observed on any of the 17 nights, even though the
likelihood of a typical LBL showing such INOV levels in a single session of
$\ga 4$ hours duration is known to be high ($\sim50%$). Our observations have
thus established a peculiar long-term INOV quiescence of this radio-selected BL
Lac object. Moreover, the access to unpublished optical monitoring data of
similarly high sensitivity, acquired in another programme, has allowed us to
confirm the same anomalous INOV quiescence of this LBL all the way back to
1989, the epoch of its historically largest radio outburst. Here, we present
observational evidence revealing the very unusual INOV behaviour of this
classical BL Lac object and discuss this briefly in the context of its other
known exceptional properties.
