Scott,

It was Tandy which sold under the Radio Shack brand(*). The TRS-80 series did indeed use the Z80 CPU, at various clock speeds in different models. Here's a link to the TRS-80 Model I .

I'd seen the Model I in magazines when it was launched, and actually got to "play" with one. I was about 11, and in the town in which I lived at that time there was a computer place. None of the glitzy stores of today, of course [Linked Image] -- It was a dingy little old back-street store with dusty windows, and all sorts of bits and pieces stacked everywhere. A real computer store, in other words! [Linked Image]

(*)An aside: We had their stores in Britain, but they went under the Tandy name rather than Radio Shack.