The flow of superfluid 4He around a translationally oscillating sphere, levitating without mechanical support, can either be laminar or turbulent, depending on the velocity amplitude. Below a critical velocity vc that scales as ω1/2 and is temperature independent below 1 K, the flow is laminar (potential flow). Below 0.5 K, the linear drag force is caused by ballistic phonon scattering that vanishes as T4 until background damping, measured in the empty cell, becomes dominant for T<0.1 K. Increasing the velocity amplitude above vc leads to a transition from potential flow to turbulence, where the large turbulent drag force varies as (v2−v2c). In a small velocity interval Δv/vc≤3% above vc, the flow is unstable below 0.5 K, switching intermittently between both patterns. From time series recorded at constant temperature and driving force, the lifetimes of both phases are analyzed statistically. We observe metastable states of potential flow which, after a mean lifetime of 25 min, ultimately break down due to vorticity created by natural background radioactivity. The lifetimes of the turbulent phases have an exponential distribution, and the mean increases exponentially with Δv2. We investigate the frequency at which the vortex rings are shed from the sphere. Our results are compared with recent data of other authors on vortex shedding by moving a laser beam through a Bose–Einstein condensate. Finally, we show that our observed transition to turbulence belongs to the class of “supertransient chaos” where lifetimes of the turbulent states increase faster than exponentially.