Can Hyper-V run in a virtual machine?

Yes, it can, if the underlying CPUs support the latest virtualization extensions (Intel VT-X/EPT) and if you're using the latest VMware products (Workstation 8, ESXi 5).

The relevant settings in your VM should be as follows:

monitor.virtual_mmu = "hardware"
monitor.virtual_exec = "hardware"
vhv.enable = "TRUE"
hypervisor.cpuid.v0 = "FALSE"

The first three settings can be enabled via GUI (where exactly varies slightly between Workstation and ESXi), the last one needs to be manually added to the VM's .vmx file.

Additionally, on ESXi 5, you need to add the following line to /etc/vmware/config:

vhv.allow = "TRUE"

There are different answers to this question.

Before WS2016/W10, the correct answer was: Yes, you can enable the Hyper-V role in a Hyper-V VM, but the hypervisor would not start. Therefore, you could create VMs in the vHost, but those VMs could not start.

However, in Windows 10 and WS2016 (TP4 and later) we can use nested Hyper-V. If you're mad enough to try, you can create a host, in a host, in a host, in a host, on a host ...