A trip to Chester Record Office proved very interesting in regards to a very early ancestor. While looking at the Church warden accounts for St. Mary-on-the-Hill, Chester I came across the following entry for Easter 1562-1563 were payments are made for 'kneeling places' by one Richard Gronow.
This is a very good early reference to an Elizabethan Gronow, that I have found. More research is needed to establish the origins of this gentleman.

{The Parish of St.Mary-on-the-Hill, Chester, extends beyond the city boundaries, and includes the township of Gloverstone, which is wholly within the city, and those of Upton, Moston, Claverton and Marleston-cum-Lache in Broxton Hundred, and Little Mollington in Wirral Hundred.}