Caching popular contents at base stations (BSs) of a heterogeneous cellular network (HCN) avoids frequent information passage from content providers to the network edge, thereby reducing latency and alleviating traffic congestion in backhaul links. In general, the optimal strategies for content placement in HCNs remain largely unknown and deriving them forms the theme of this paper. To this end, we adopt the popular random HCN model where $K$ tiers of BSs are modelled as independent Poisson point processes distributed in the plane with different densities. Further, the random caching scheme is considered where each of a given set of $M$ files with corresponding popularity measures is placed at each BS of a particular tier with a corresponding probability, called placement probability. The probabilities are identical for all BSs in the same tier but vary over tiers, giving the name tier-level content placement. We consider the network performance metric, hit probability, defined as the probability that a file requested by the typical user is delivered successfully to the user. We maximize the hit probability over content placement probabilities, which yields the optimal tier-level placement policies. For the case of uniform received signal-to-interference thresholds for successful transmissions for BSs in different tiers, the policy is in closed-form where the placement probability for a particular file is proportional to the square-root of the corresponding popularity measure with an offset depending on BS caching capacities. For the general case of non-uniform SIR thresholds, the optimization problem is non-convex and a sub-optimal placement policy is designed by approximation, which has a similar structure as in the case of uniform SIR thresholds and shown by simulation to be close-to-optimal.