  Blue large-amplitude pulsators (BLAPs) form a small group of hot objects
pulsating in a fundamental radial mode with periods of the order of 30 minutes.
Proposed evolutionary scenarios explain them as evolved low-mass stars: either
~0.3 M$_\odot$ shell-hydrogen-burning objects with a degenerated helium core,
or more massive (0.5 - 0.8) M$_\odot$ core-helium-burning stars, or ~0.7
M$_\odot$ surviving companions of type Ia supernovae. Therefore, their origin
remains to be established. Using data from Transiting Exoplanet Survey
Satellite, we discovered that HD 133729 is a binary consisting of a late B-type
main-sequence star and a BLAP. The BLAP pulsates with a period of 32.37 min
decreasing at a rate of $(-7.11 \pm 0.33)\times 10^{-11}$. Due to light
dilution by a brighter companion, the observed amplitude of pulsation is much
smaller than in other BLAPs. From available photometry, we derived times of
maximum light, which revealed the binary nature of the star via O-C diagram.
The diagram shows variations with a period of 23.08433 d that we attribute to
the light-travel-time effect in the system. The analysis of these variations
allowed to derive the spectroscopic parameters of the BLAP's orbit around the
center of the mass of the binary. The presence of a hot companion in the system
was confirmed by the analysis of its spectral energy distribution, which was
also used to place the components in the H-R diagram. The obtained position of
the BLAP fully agrees with the location of the other members of the class. With
the estimated V~11 mag and the Gaia distance of less than 0.5 kpc, the BLAP is
the brightest and the nearest of all known BLAPs. It may become a clue object
in the verification of the evolutionary scenarios for this class of variable.
We argue that low-mass progenitors of the BLAP are excluded if the components
are coeval and no mass transfer between the components took place.
