Constraints on the intrinsic charm probability $w = P_{c\bar c / p}$ in the proton are obtained for the first time from LHC measurements. ATLAS Collaboration data for the production of prompt photons, accompanied by a charm-quark jet in pp collisions at $\sqrt s = 8 $ TeV are used. Fits to the ATLAS data result in a central estimate: $w = 1.14\%$. Upper limits: $w < 2.74\%$ ($4.32\%$) are obtained at the $68\% (95\%) $ C.L. The results, however, do not rule out zero intrinsic charm at one standard deviation. We suggest methods which can reduce the uncertainties for determining the intrinsic charm probability, such as the elimination of theoretical scale ambiguities and tests of $x_T = 2 E_T^\gamma / \sqrt{s}$ - scaling at fixed rapidity, as well as measurements of the $x_T$ distribution at different LHC energies. Other implications of intrinsic heavy quarks in the proton for QCD studies at the LHC are also discussed. Show Partial Abstract