Is a chronograph necessary? That depends on what is important to you.
As many have wisely said, start low, find an accurate load, and the target won't care. If that describes you, you can do without a chronograph.
If, on the other hand, it is important to you to know what your load is doing, you will need a chronograph. For rifles, the MV out of your rifle may be hundreds of fps off of what is listed in the manual. You can't rely on the manuals to tell you what is going to happen with your rifle. For pistols the situation is less extreme (10% slow at 1000 fps is slow by 100 fps, 10% slow at 3000 fps is slow by 300 fps!) but may still exceed what you are comfortable with.
Try reloading without a chronograph at first (except, as RC noted, you need to have proof of reaching a set power factor). If you are satisfied, great. If you're left with a nagging feeling of uncertainty, spring for a chronograph. That's my $0.02.
Good Luck,
Dan