I am looking for an old comedy movie from the late 50?s or early 60?s.
 I think it stared either Bob Hope or Danny Kaye.  There is a chase
scene in it which involves the main character and a woman running away
from gangsters or the mob.  They commandeer a lumber carrier* as the
mode of transportation.  The chase scene is hilarious as they drive
recklessly through the town and even into a river to evade capture.


*I doubt it if these type of vehicles even exist any more.  A description follows:

A lumber carrier is a vehicle which stands on four legs about 8 feet
high, each with a wheel attached.  Imagine a rectangle coffee table
with wheels on each leg.  The drive would sit on the top of the table
to drive it.  A lumber carrier is used to move a stack of lumber from
one spot to another.  This vehicle would drive over a stack of lumber,
grasp it from the bottom, lift it up slightly and transport it to
another location.  A photo can be found at this website:
http://www.lincolncountylibraries.com/museum/lumber_carrier.htm

I doubt if it was either Danny Kaye or Bob Hope.

Maybe more slapstick a la Red Skelton or Buster Keaton?

Could it be "The Ghost Breakers" with Bob Hope and Paulette Goddard:
http://www.imdb.com/title/tt0032520/plotsummary

The plot involves and man and woman and the mob.

Are you talking about "The Secret Life of Walter Mitty"?  this
starrred Danny Kaye and if I remember correctly had a chase seen in it
dealing with the mob.

Is it "The Man From the Diner's Club" (1963) starring Danny Kaye. It's
pretty 'slapsticky' if I remember and I'm sure it has a chase
involving the mob.