Homeostatic plasticity is a stabilizing mechanism commonly observed in real neural systems that allows neurons to maintain their activity around a functional operating point. This phenomenon can be used in neuromorphic systems to compensate for slowly changing conditions or chronic shifts in the system configuration. However, to avoid interference with other adaptation or learning processes active in the neuromorphic system, it is important that the homeostatic plasticity mechanism operates on time scales that are much longer than conventional synaptic plasticity ones. In this paper we present an ultralow leakage circuit, integrated into an automatic gain control scheme, that can implement the synaptic scaling homeostatic process over extremely long time scales. Synaptic scaling consists in globally scaling the synaptic weights of all synapses impinging onto a neuron maintaining their relative differences, to preserve the effects of learning. The scheme we propose controls the global gain of analog log-domain synapse circuits to keep the neuron's average firing rate constant around a set operating point, over extremely long time scales. To validate the proposed scheme, we implemented the ultralow leakage synaptic scaling homeostatic plasticity circuit in a standard 0.18 μm complementary metal-oxide-semiconductor process, and integrated it in an array of dynamic synapses connected to an adaptive integrate and fire neuron. The circuit occupies a silicon area of 84 μm × 22 μm and consumes approximately 10.8 nW with a 1.8 V supply voltage. We present experimental results from the homeostatic circuit and demonstrate how it can be configured to exhibit time scales of up to 100 ks, thanks to a controllable leakage current that can be scaled down to 0.45 aA (2.8 electrons per second).