A 303-MHz hyperfine transition in the ground state of 9Be+ was used as a basis of a frequency standard. The ions were stored in a Penning ion trap. Linewidths as narrow as 900μHz were obtained. The frequency stability was measured to be better than 3 x 10-12τ-1/2. The inaccuracy in the second-order .Doppler shift was reduced to 5 parts in 1015 by laser cooling. An apparent pressure shift with an unexpectedly large value was discovered which limits the accuracy of the current experiment to approximately 1 part in 1013.