The bin packing problem is defined as follows: given a set of n items with sizes 0 < w 1 , w 2 , … , w n ≤ 1 , find a packing of these items into a minimum number of unit-size bins possible. We present a sublinear-time asymptotic approximation scheme for the bin packing problem; that is, for any ϵ > 0 , we present an algorithm A ϵ that has sampling access to the input instance and outputs a value k such that C opt ≤ k ≤ ( 1 + ϵ ) ⋅ C opt + 1 , where C opt is the cost of an optimal solution. It is clear that uniform sampling by itself will not allow a sublinear-time algorithm in this setting; a small number of items might constitute most of the total weight and uniform samples will not hit them. In this work we use weighted samples, where item i is sampled with probability proportional to its weight: that is, with probability w i / ∑ i w i . In the presence of weighted samples, the approximation algorithm runs in O ̃ ( n ⋅ poly ( 1 / ϵ ) ) + g ( 1 / ϵ ) time, where g ( x ) is an exponential function of x . When both weighted sampling and uniform sampling are allowed, O ̃ ( n 1 / 3 ⋅ poly ( 1 / ϵ ) ) + g ( 1 / ϵ ) time suffices. In addition to an approximate value to C opt , our algorithm can also output a constant-size “template” of a packing that can later be used to find a near-optimal packing in linear time.