  The effect of an hexagonal boron nitride (hBN) layer close aligned with
twisted bilayer graphene (TBG) is studied. At sufficiently low angles between
twisted bilayer graphene and hBN, $\theta_{hBN} \lesssim 2^\circ$, the graphene
electronic structure is strongly disturbed. The width of the low energy peak in
the density of states changes from $W \sim 5 - 10$ meV for a decoupled system
to $\sim 20 - 30$ meV. Spikes in the density of states due to van Hove
singularities are smoothed out. We find that for a realistic combination of the
twist angle in the TBG and the twist angle between the hBN and the graphene
layer the system can be described using a single moir\'e unit cell.

Strongly Correlated Electrons;Mesoscale and Nanoscale Physics