Do 74HCxx chips require a linear voltage generator?
There is no requirement that would require a linear regulator for 74HCx. You should read the family spec to assure yourself.

Read section 5 on the voltage ratings.

In particular look at Figure 16 which shows the family VCC relationship.

If you are using 74HC devices then they are rated for operation from 2 - 6 V  ....but if you are using 74HCT then the device is only rated for 5 V +/-10% ....many do confuse this. The 74HCT devices can be mixed with 74LS TTL devices, while the 74HC are not guaranteed to interoperate with the same fanouts when mixed. 

If you are mixing 74LS and 74HCT devices, you may have difficulties meeting the +/-5% VCC tolerance of the 74LS devices (ripple from switching regulators) but should have no problems for 74HC devices.