Using nested-grid, high-resolution 3-D hydrodynamic simulations of gas and particle dynamics in the vicinity of Mars- to Earth-mass planetary embryos, we show that rocky planets such as Earth and Mars can form in of the order of 1 Myr, by accreting solids in the form of mm-size chondrules, rather than the cm-dm size solids that are often assumed in “pebble accretion” models. The simulations (detailed in Popovas et al, 2018MNRAS.479.5136P and 2019MNRAS.482L.107P) extend from the surface of the embryos to a few vertical disc scale heights, with a spatial dynamic range of order 105. We find that, due to cancellation effects, accretion rates are to lowest order independent of disc surface density, while varying inversely with particle size. As a result, we can estimate accurate growth times for specified particle sizes. For 0.3-1 mm size particles the growth time from a small seed is about 1.5 million years for an Earth-mass planet at 1 au and about 1 million years for a Mars mass planet at 1.5 au. These finding, which are robust – given only the assumptions that accretion takes place in a local pressure maximum (“pressure trap”) and that the dust-to-gas ratio is at least of order 1% – are significant, since it is well known from meteoritic studies that chondrules were abundantly present in the early solar system, and because it has recently been shown by cosmochemical analysis that most chondrules formed in the first million year after formation of the solar system.