CHY Calamos Convertible and High Income Fund

Amendment to Prospectus Supplement

(To Prospectus dated March 1, 2021)

Calamos Convertible and High Income Fund (the “Fund”)

Supplement dated September 30, 2021 to the Fund’s Prospectus dated March 1, 2021, and
as supplemented March 5, 2021 and August 27, 2021

All references in the Prospectus Supplement to the Distribution Agreement shall mean the distribution agreement effective as of September 30, 2021 between Calamos Convertible and High Income Fund and Foreside Fund Services, LLC (the “Distributor”).

The Fund and the Distributor entered into the new Distribution Agreement due to a change of control of the Distributor.  A majority of the interests of Foreside Financial Group, LLC, the indirect parent of the Distributor, are being sold to GC Mountaintop Acquisition Corp., an affiliate of Genstar Capital (the “Transaction”).  The Transaction is not expected to have any operational impact on the Distributor and the services that the Distributor provides to the Fund will not change.  The terms of the new Distribution Agreement are identical to the terms of the prior Distribution Agreement.

In addition, all references in the Prospectus Supplement to the Sub-Placement Agent Agreement shall mean the Sub-Placement Agent Agreement effective as of September 30, 2021 between the Distributor and UBS Securities LLC (the “Sub-Placement Agent”).  The terms of the new Sub-Placement Agent Agreement are identical to the terms of the prior Sub-Placement Agent Agreement.

Please retain this supplement for future reference.