Take a binary counter, compute some ugly logical function from its output.

The problem is that "ugly" functions have a long history of being
not as random as you would like.

You could use a ROM and some software to generate the contents.
But I don't know any 74HC parts that are ROMs.

LFSR is best solution to Jim's problem that I know of.

--
These are my opinions, not necessarily my employer's. I hate spam.