  Strong measurements usually restrict the dynamics of measured finite
dimensional systems to the Zeno subspace, where subsequent evolution is unitary
due to the suppression of dissipative terms. Here we show qualitatively
different behaviour due to the competition between strong measurements and the
thermodynamic limit, inducing a time-translation symmetry breaking phase
transition resulting in a continuous time crystal. We consider a spin star
model, where the central spin is subject to a strong continuous measurement,
and qualify the dynamic behaviour of the system in various parameter regimes.
We show that above a critical value of measurement strength, the magnetization
of the thermodynamically large ancilla spins develops limit cycle oscillations.
Our result also demonstrates that a coherent drive is not necessary in order to
induce continuous time-translation symmetry breaking.
