In this first systematic attempt to characterise the intranight optical variability (INOV) of TeV detected blazars, we have monitored a well defined set of 9 TeV blazars on total 26 nights during 2004-2010. In this R (or V)-band monitoring programme only one blazar was monitored per night for a minimum duration of 4 hours. Using the CCD, an INOV detection threshold of ~ 1-2 % was achieved in the densely sampled DLCs. We have further expanded the sample by including another 13 TeV blazars from literature. This enlarged sample of 22 TeV blazars, monitored on a total of 116 nights (including 55 nights newly reported here), has enabled us to arrive at the first estimate of the INOV duty cycle of TeV detected blazars. Applying the C-test, the INOV DC is found to be 59 %, which decreases to 47 % if only INOV fractional amplitudes above 3 % are considered. These observations also permit, for the first time, a comparison of the INOV characteristics of the two major subclasses of TeV detected BL Lacs, namely LBLs and HBLs, for which we find the INOV DCs to be ~ 63 % and ~ 38 %, respectively. This demonstrates that the INOV differential between LBLs and HBLs persists even when only their TeV detected subsets are considered. Despite dense sampling, the intranight light curves of the 22 TeV blazars have not revealed even a single feature on time scale substantially shorter than 1 hour, even though the inner jets of TeV blazars are believed to have exceptionally large bulk Lorentz factors (and correspondingly stronger time compression). An intriguing feature, clearly detected in the light curve of the HBL J1555+1111, is a 4 per cent `dip on a 1 hour timescale. This unique feature could have arisen from absorption in a dusty gas cloud, occulting a superluminally moving optical knot in the parsec scale jet of this relatively luminous BL Lacs object.
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