chol[A_] :=
 Module[{L},
  L[k_, k_] := L[k, k] = Sqrt[A[[k, k]] - Sum[L[k, j]^2, {j, 1, k-1}]];
  L[i_, k_] := L[i, k] = L[k, k]^-1 (A[[i, k]] - Sum[L[i, j] L[k, j], {j, 1, k-1}]);
  PadRight[Table[L[i, j], {i, Length[A]}, {j, i}]]
 ]