The static capacity provisioning in traditional WiFi networks (WLANs) cannot cope with the high spatiotemporal traffic variations in high-density venues such as conference centers, stadiums etc. To guarantee reliable performance, venue owners are forced to over-provision their WLANs based on worst-case traffic demand estimations, increasing capital and operational expenses. We propose AmorFi, a radically new way of deploying WLANs to handle peak traffic demands with average-case provisioning. Our key idea is to decouple baseband processing from RF transmission (inspired by the cloud-RAN concept in cellular networks) and introduce software programmability to flexibly allocate WiFi capacity in real time based on varying traffic demands. We implement AmorFi using off-the-shelf WiFi APs over a RF-over-fiber cloud-RAN testbed. Our experiments and simulations demonstrate that the software-defined capacity allocation enabled with AmorFi delivers more than throughput than traditional WLANs.