diff --git a/bilby/gw/prior.py b/bilby/gw/prior.py
index 8d8f360e3e65f20fc6d7e84a4af93b7d68bb63dc..9eac23a5cdcfd4010abf36faa45def3509c95c55 100644
--- a/bilby/gw/prior.py
+++ b/bilby/gw/prior.py
@@ -229,7 +229,10 @@ class AlignedSpin(Interped):
                       a_prior.minimum * z_prior.maximum)
         chi_max = a_prior.maximum * z_prior.maximum
         xx = np.linspace(chi_min, chi_max, 800)
-        aas = np.linspace(a_prior.minimum, a_prior.maximum, 1000)
+        a_prior_minimum = a_prior.minimum
+        if a_prior_minimum == 0:
+            a_prior_minimum += 1e-32
+        aas = np.linspace(a_prior_minimum, a_prior.maximum, 1000)
         yy = [np.trapz(np.nan_to_num(a_prior.prob(aas) / aas *
                                      z_prior.prob(x / aas)), aas) for x in xx]
         super(AlignedSpin, self).__init__(xx=xx, yy=yy, name=name,