......on the chip and the category of collector.
Someone who collects rock and roll memorabilia would generally pay more for an autographed, but common Hard Rock chip than a chip collector would.

Now if the Hard Rock chip was a hard to get example, the chip collector definitely would pay more without the autograph.

Of course, an unrelated autograph on a classic collectible chip will ruin its value, unless maybe it is like George Washington's signature on that 1st Issue Sahara you have....