**Exhibit 31.1** **CERTIFICATION**     I, John C. Malone, certify that:     1. I have reviewed this quarterly report on    Form 10-Q    of Discovery Holding Company;     2. Based on my knowledge, this quarterly report does not    contain any untrue statement of a material fact or omit to state    a material fact necessary to make the statements made, in light    of the circumstances under which such statements were made, not    misleading with respect to the period covered by this quarterly    report;     3. Based on my knowledge, the financial statements and    other financial information included in this quarterly report    fairly present in all material respects the financial condition,    results of operations and cash flows of the registrant as of,    and for, the periods presented in this quarterly report;     4. The registrant’s other certifying officers and I    are responsible for establishing and maintaining disclosure    controls and procedures (as defined in Exchange Act    Rules 13a-15(e)    and    15d-15(e))    and internal control over financial reporting (as defined in    Exchange Act    Rules 13a-15(f)    and    15d-15(f))    for the registrant and we have:     a) designed such disclosure controls and procedures, or    caused such disclosure controls and procedures to be designed    under our supervision, to ensure that material information    relating to the registrant, including its consolidated    subsidiaries, is made known to us by others within those    entities, particularly during the period in which this quarterly    report is being prepared;     b) designed such internal control over financial reporting,    or caused such internal control over financial reporting to be    designed under our supervision, to provide reasonable assurance    regarding the reliability of financial reporting and the    preparation of financial statements for external purposes in    accordance with generally accepted accounting principles;     c) evaluated the effectiveness of the registrant’s    disclosure controls and procedures and presented in this    quarterly report our conclusions about the effectiveness of the    disclosure controls and procedures as of the end of the period    covered by this quarterly report based on such    evaluation; and     d) disclosed in this quarterly report any change in the    registrant’s internal control over financial reporting that    occurred during the registrant’s most recent fiscal quarter    (the registrant’s fourth fiscal quarter in the case of an    annual report) that has materially affected, or is reasonably    likely to materially affect, the registrant’s internal    control over financial reporting; and     5. The registrant’s other certifying officers and I    have disclosed, based on our most recent evaluation of internal    control over financial reporting, to the registrant’s    auditors and the audit committee of the registrant’s board    of directors (or persons performing the equivalent function):     a) all significant deficiencies and material weaknesses in    the design or operation of internal control over financial    reporting which are reasonably likely to adversely affect the    registrant’s ability to record, process, summarize and    report financial information; and     b) any fraud, whether or not material, that involves    management or other employees who have a significant role in the    registrant’s internal control over financial reporting.     Date: May 8, 2008/s/  John    C. Malone    John C. Malone    Chief Executive Officer